First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually.

Problem 5-1 Simple Interest versus Compound Interest [LO1]

First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually.

  

If you made a $67,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 9 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Difference in accounts

$

 

Explanation:

The time line for the cash flows is:

   

0		9
$67,000		FV

The simple interest per year is:

$67,000 × .07 = $4,690

So after 9 years you will have:

$4,690 × 9 = $42,210 in interest.

The total balance will be $67,000 + 42,210 = $109,210

With compound interest we use the future value formula:

FV = PV(1 + r)t

FV = $67,000(1.07)9 = $123,176.77

The difference is:

$123,176.77 – 109,210 = $13,966.77

Calculator Solution:

 

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

 

Enter

9

7%

±$67,000

N

I/Y

PV

PMT

FV

Solve for

$123,176.77

$123,176.77 − 109,210 = $13,966.77

Tai Credit Corp. wants to earn an effective annual return on its consumer loans of 14.4 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers?

Problem 6-15 Calculating APR [LO4]

Tai Credit Corp. wants to earn an effective annual return on its consumer loans of 14.4 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? (Use 365 days a year. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Interest rate

%

 

Explanation:

The reported rate is the APR, so we need to convert the EAR to an APR as follows:

EAR = [1 + (APR / m)]m − 1

APR = m[(1 + EAR)1/m − 1]

APR = 365[(1.144)1/365 − 1]

APR = .1346, or 13.46%

This is deceptive because the borrower is actually paying annualized interest of 14.4 percent per year, not the 13.46 percent reported on the loan contract.

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  

Enter				14.4%			365
		NOM			EFF			C/Y
Solve for	13.46%