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# APR and Interest Rates

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1. Three students each have \$1000 to invest from their summer jobs. Armen invests his money in an account that earns simple interest at an APR of 5 percent. Barok invests his money in an account that earns 4.9 percent interest per year compounded annually. Carrie invests her money in an account that earns 4.8 percent interest per year compounded monthly. Find how much money each student has in his or her account after
A) 2 years
B) 10 years
C) 30 years

2. Here's an old story: A man walks into a New York City bank and asks for a \$5000 loan, offering his Ferrari, worth \$250,000 as collateral. He tells the loan officer that he needs the money for two weeks for an important venture. The loan officer, having the car as security and after checking references, gives the man the money he requested, with a signed agreement that he will pay the money plus \$45 in interest when he returns in two weeks. The bank officer takes the car keys and the car is parked in the bank's underground lot. The man returns in exactly two weeks, pays the loan and interest, and reclaims his car. The bank officer asked him why he was willing to pay such a high interest rate. His reply: where else can I safely park my car for two weeks in New York City for only \$45?
A) What annual interest rate did the man pay?
B) How much would the man need to repay at the end of two months if he borrowed \$5000 with the same rules and same annual interest rate?

6. A new parent wants to have \$80,000 in a college savings account in 18 years. Although it's difficult to predict what the APR will be over 18 years, we can get a sense of how much the parent should save each month using various assumptions. Calculate the monthly savings needed if the money is invested in an account with monthly compounding and an APR of
A) 4 percent
B) 7 percent
C) 9 percent

Please see the attached file for details.

#### Solution Preview

Exploration 1, 2 and 6

1. Three students each have \$1000 to invest from their summer jobs. Armen invests his money in an account that earns simple interest at an APR of 5 percent. Barok invests his money in an account that earns 4.9 percent interest per year compounded annually. Carrie invests her money in an account that earns 4.8 percent interest per year compounded monthly. Find how much money each student has in his or her account after

APR= Annual percentage rate
EAR= Effective annual rate

Armen= 5% Simple Interest
Barok:
EAR= 4.90% (since annual compounding)
Carrie:
EAR= 4.9070% =(1+4.8%/12)^12-1 (^ means raised to the power of)

With simple interest ; Amount = Principal x (1+ simple interest x T)
With compound interest ; Amount = Principal x (1+ EAR)^T

Principal= \$1,000

A) 2 years

Time= 2 years

Armen= \$1,100.00 =1000 x (1+5.%) x 2
Barok= \$1,100.40 =1000 x (1+4.9%) ^ 2
Carrie: \$1,100.55 =1000 x (1+4.907%) ^ 2

Answer: Amount at the end of 2 years

Armen= \$1,100.00
Barok= \$1,100.40
Carrie: \$1,100.55

B) 10 years

Time= 10 years

Armen= \$1,500.00 =1000 x (1+5.%) x 10
Barok= \$1,613.45 =1000 x (1+4.9%) ^ 10
Carrie: \$1,614.52 =1000 x ...

#### Solution Summary

Interest calculations for different rates and different time periods have been carried out.

\$2.19