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