# julie and kalyn both invested $10,000 5 years ago. they both earned a 8% return, however julie earned a simple return of 8% and kalyn earned a compounded return of 8%. how did this difference in compounding affect their investments’ value today?

### James

Guys, does anyone know the answer?

get julie and kalyn both invested $10,000 5 years ago. they both earned a 8% return, however julie earned a simple return of 8% and kalyn earned a compounded return of 8%. how did this difference in compounding affect their investments’ value today? from EN Bilgi.

## Compound Interest Calculator

Compound interest calculator. Here's how to use NerdWallet’s calculator to determine how much your money can grow with compound interest.

## Compound Interest Calculator

Margarette Burnette November 24, 2021

### Future Balance

## $11,000

Year Now 2024 2026 Balance $0 $2,400 $4,800 $7,300 $9,700 $12,000 PrincipalInterest

## Save more money.

Use NerdWallet to find a better bank account.

FIND AN ACCOUNT

It pays to have a Nerdy expert

With a NerdWallet Plus subscription, get financial coaching, identity theft protection, and custom budgeting tools — all approved by the Nerdy experts.

LEARN ABOUT NERDWALLET PLUS

The investing information provided on this page is for educational purposes only. NerdWallet does not offer advisory or brokerage services, nor does it recommend or advise investors to buy or sell particular stocks, securities or other investments.

ALSO CONSIDER: Savings Calculator || Emergency Fund Calculator || CD Calculator

Your savings account balances and investments can grow more quickly over time through the magic of compounding. Use the compound interest calculator above to see how big a difference it could make for you.

## Using this compound interest calculator

Try your calculations both with and without a monthly contribution — say, $50 to $200, depending on what you can afford.

This savings calculator includes a sample rate of return. To see the interest you can expect, compare rates on NerdWallet.

» Ready to begin? Start saving with some of our favorite savings accounts or IRA providers

LEARN MORE Member FDIC

LendingClub High-Yield Savings

APY 0.65%

Min. balance for APY

$2,500 LEARN MORE Member FDIC

Synchrony Bank High Yield Savings

APY 0.60%

Min. balance for APY

$0 LEARN MORE Member FDIC

American Express® High Yield Savings Account

APY 0.50%

Min. balance for APY

$1

EXPLORE MORE ACCOUNTS

Here’s a deeper look at how compounding works:

## What is compound interest?

For savers, the definition of compound interest is basic: It’s the interest you earn on both your original money and on the interest you keep accumulating. Compound interest allows your savings to grow faster over time.

In an account that pays compound interest, such as a standard savings account, the return gets added to the original principal at the end of every compounding period, typically daily or monthly. Each time interest is calculated and added to the account, the larger balance earns more interest, resulting in higher yields.

For example, if you put $10,000 into a savings account with a 0.50% annual yield, compounded daily, you’d earn $51 in interest the first and second years, and $53 the third year. After 10 years of compounding, you would have earned a total of $513 in interest.

But remember, that’s just an example. For longer-term savings, there are better places than savings accounts to store your money, including Roth or traditional IRAs and CDs.

## Compounding investment returns

When you invest in the stock market, you don’t earn a set interest rate but rather a return based on the change in the value of your investment. When the value of your investment goes up, you earn a return.

If you leave your money and the returns you earn invested in the market, those returns are compounded over time in the same way that interest is compounded.

If you invested $10,000 in a mutual fund and the fund earned a 7% return for the year, you’d gain about $700, and your investment would be worth $10,700. If you got an average 7% return the following year, your investment would then be worth about $11,500.

Over the years, your investment can really grow: If you kept that money in a retirement account over 30 years and earned that average 7% return, for example, your $10,000 would grow to more than $76,000.

In reality, investment returns will vary year to year and even day to day. In the short term, riskier investments such as stocks or stock mutual funds may actually lose value. But over a long time horizon, history shows that a diversified growth portfolio can return an average of 6% to 7% annually. Investment returns are typically shown at an annual rate of return.

The average stock market return is historically 10% annually, though that rate is reduced by inflation. Investors can currently expect inflation to reduce purchasing power by 2% to 3% a year.

Compounding can help fulfill your long-term savings and investment goals, especially if you have time to let it work its magic over years or decades. You can earn far more than what you started with.

» Explore more: Find rates for thousands of savings accounts and certificates of deposit

## More NerdWallet calculators

Home affordability Mortgage payment Down payment Student loans Retirement

## Compounding with additional contributions

As impressive as compound interest might be, progress on savings goals also depends on making steady contributions.

Let’s go back to the savings account example above. We started with $10,000 and ended up with a little more than $500 in interest after 10 years in an account with a 0.50% annual yield. But by depositing an additional $100 each month into your savings account, you’d end up with $21,821 after 10 years, when compounded daily. The interest would be $821 on total deposits of $22,000.

## FIN 301 Exam 2 Flashcards

Start studying FIN 301 Exam 2. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## FIN 301 Exam 2

10 studiers in the last hour

Which of the following is a primary disadvantage to investing in a hedge fund?

a) Hedge funds invest in only stocks

b) Hedge funds use advanced investment strategies

c) Illiquidity

d) Hedge funds invest in only bonds

e) Lax regulation

Click card to see definition 👆

c) Illiquidity

Click again to see term 👆

Which of the following is true concerning the difference between simple and compound interest?

a) With compound interest, interest is earned only on the original investment whereas with simple interest, interest is earned on interest.

b) Simple interest always leads to a higher ending investment value when compared to compound interest.

c) With simple interest, interest is earned only on the original investment whereas with compound interest, interest is earned on both the original investment and the accumulated interest.

d) With compound interest, the assumption is that interest earned on the original investment is not reinvested. With simple interest, interest is reinvested.

e) Simple interest and compound interest always lead to the same ending investment value so there is no difference between the two methods.

Click card to see definition 👆

c) With simple interest, interest is earned only on the original investment whereas with compound interest, interest is earned on both the original investment and the accumulated interest.

Click again to see term 👆

1/25 Created by torimyirski

### Terms in this set (25)

Which of the following is a primary disadvantage to investing in a hedge fund?

a) Hedge funds invest in only stocks

b) Hedge funds use advanced investment strategies

c) Illiquidity

d) Hedge funds invest in only bonds

e) Lax regulation c) Illiquidity

Which of the following is true concerning the difference between simple and compound interest?

a) With compound interest, interest is earned only on the original investment whereas with simple interest, interest is earned on interest.

b) Simple interest always leads to a higher ending investment value when compared to compound interest.

c) With simple interest, interest is earned only on the original investment whereas with compound interest, interest is earned on both the original investment and the accumulated interest.

d) With compound interest, the assumption is that interest earned on the original investment is not reinvested. With simple interest, interest is reinvested.

e) Simple interest and compound interest always lead to the same ending investment value so there is no difference between the two methods.

If you are selling a stock, which of the following bid prices is the most attractive?

a) 20.70-21.15 b) 20.72-21.17 c) 20.71-21.16 d) 20.77-21.22 e) 20.74-21.11 d) 20.77-21.22

Mr. Wonderful needs $3,000,000 upon retirement in 10 years to live comfortably. He can invest $130,000 a year to his retirement. What interest rate would his investment need to earn in order for him to meet his goals?

a) 4.8% b) 13.7% c) 17.6% d) 23.7%

e) This plan is not feasible

c) 17.6%

Suppose your investment returns are taxed at a 15% rate. If you invest $100,000 today and expect to earn a rate of return of 7%, what will your investment be worth in 25 years?

a) $684,847 b) $108,000 c) $106,400 d) $424,154 e) $148,711 d) $424,154

What interest rate would you have to earn if you wanted to triple an investment in 12 years?

a) 5.7% b) 9.6% c) 17.6% d) 13.3% e) 7.6% b) 9.6%

According to the financial life cycle, which of the following is the first source of capital for a business?

a) Bank financing b) Owner's capital c) Private Equity d) Bond offerings e) Venture capital b) Owner's capital

What is the following is true about the S&P 500?

a) The largest sector in the S&P 500 is the financial sector

b) The S&P 500 is the best known stock market index

c) The S&P 500 weights stocks by their market price

d) The S&P 500 is composed of the 500 companies with the highest annual sales

e) The S&P 500 weights stocks by their market value

e) The S&P 500 weights stocks by their market value

Which of the following transactions would take place in the secondary securities market?

a) An investor buys a stock from another investor.

b) An investor buys an IPO stock through an investment bank.

c) An investor buys a secondary offering stock from the issuing company.

d) Profits from newly issued securities benefit the issuing company, not the investors.

e) An investor buys a bond from Ford.

a) An investor buys a stock from another investor.

Julie and Kalyn both invested $10,000 5 years ago. They both earned a 7% return, however Julie earned a simple return of 7% and Kalyn earned a compounded return of 7%. How did this difference in compounding affect their investments' value today?

a) Julie will have $693 more than Kalyn

b) Kalyn will have $693 more than Julie

## Simple and Compound Interest – Math For Our World

## SIMPLE AND COMPOUND INTEREST

### Learning Outcomes

Calculate one-time simple interest, and simple interest over time

Determine APY given an interest scenario

Calculate compound interest

We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for retirement, or need a loan, we need more mathematics.

## SIMPLE INTEREST

Discussing interest starts with the **principal**, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.

### Simple One-time Interest

(1) I is the interest

A is the end amount: principal plus interest

(2)

is the principal (starting amount)

r is the interest rate (in decimal form. Example: 5% = 0.05)

### Examples

A friend asks to borrow $300 and agrees to repay it in 30 days with 3% interest. How much interest will you earn?

**Solution:**

(3) = $300 the principal r = 0.03 3% rate

I = $300(0.03) = $9. You will earn $9 interest.

The following video works through this example in detail.

One-time simple interest is only common for extremely short-term loans. For longer term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be earned regularly.

For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.

### Exercises

Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?

[reveal-answer q=”14596″]Show Solution[/reveal-answer]

[hidden-answer a=”14596″]Each year, you would earn 5% interest: $1000(0.05) = $50 in interest. So over the course of five years, you would earn a total of $250 in interest. When the bond matures, you would receive back the $1,000 you originally paid, leaving you with a total of $1,250.[/hidden-answer]

Further explanation about solving this example can be seen here.

We can generalize this idea of simple interest over time.

### Simple Interest over Time

(4) I is the interest

A is the end amount: principal plus interest

(5)

is the principal (starting amount)

r is the interest rate in decimal form

t is time

The units of measurement (years, months, etc.) for the time should match the time period for the interest rate.

### APR – Annual Percentage Rate

Interest rates are usually given as an **annual percentage rate (APR)** – the total interest that will be paid in the year. If the interest is paid in smaller time increments, the APR will be divided up.

For example, a 6% APR paid monthly would be divided into twelve 0.5% payments.

A 4% annual rate paid quarterly would be divided into four 1% payments.

### Example

Treasury Notes (T-notes) are bonds issued by the federal government to cover its expenses. Suppose you obtain a $1,000 T-note with a 4% annual rate, paid semi-annually, with a maturity in 4 years. How much interest will you earn?

**Solution:**

Since interest is being paid semi-annually (twice a year), the 4% interest will be divided into two 2% payments.

(6) = $1000 the principal

r = 0.02 2% rate per half-year

t = 8 4 years = 8 half-years

I = $1000(0.02)(8) = $160. You will earn $160 interest total over the four years.

This video explains the solution.

### Try It

Click here to try this problem.

### Try It

A loan company charges $30 interest for a one month loan of $500. Find the annual interest rate they are charging.

**Solution:**

I = $30 of interest = $500 principal r = unknown t = 1 month

Using , we get . Solving, we get r = 0.06, or 6%. Since the time was monthly, this is the monthly interest. The annual rate would be 12 times this: 72% interest.

### Try It

Click here to try this problem.

## COMPOUND INTEREST

With simple interest, we were assuming that we pocketed the interest when we received it. In a standard bank account, any interest we earn is automatically added to our balance, and we earn interest on that interest in future years. This reinvestment of interest is called **compounding**.

Guys, does anyone know the answer?