Question

First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually. If you made a $69,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Difference in accounts $

Answer 1

Future Value of First city bank

=

P+(P*i*n)

Where,

=

69000+(69000*6%*10)

P

=

Amount deposited

=

$ 69,000

=

$1,10,400.00

i

=

Interest rate

=

6%

n

=

Life

=

10

Future Value of Second city bank

=

P*(1+i)^n

Where,

=

69000*(1+0.06)^10

P

=

Amount deposited

=

$ 69,000

=

$1,23,568.49

i

=

Interest rate

=

6%

n

=

Life

=

10

Excess return

=

$1,23,568.49

-

$1,10,400

=

$   13,168.49

Thus,

Difference in accounts

$13,168.49

The difference in return is due to nature of interest earning.

In case of simple interest earning, interest amount is same for all years.

But, when bank gives compound interest, it means bank gives first period interest on investment at beginning and after that

all period investment amount will also include interest earned in previous period.

so that interest earned after year 1 will be interest earned on interest amount also.