Question

First City Bank pays 8 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually.

If you made a $65,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 8 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Difference in accounts ______

At 6.90 percent interest, how long does it take to double your money? (Round your answer to 2 decimal places. (e.g., 32.16))

Length of time _____ years

At 6.90 percent interest, how long does it take to quadruple it? (Round your answer to 2 decimal places. (e.g., 32.16))

Length of time _______ years

Answer 1

Earns $13650 more;

To double: 14.49years at simple interest or 10.39years at compound rate.43.48years at simple interest or 20.78years at compound rate

To quadruple:

Step-by-step explanation:

Using simple interest calculation:

I=PRT/100

I=Interest

P=Principal

R=Interest Rate

T=Time

Therefore I=65000*0.08*8

I=41600

Using compound interest calculation;

A=P(1+R)^T

A=Amount

A=65000(1+0.08)^8

A=65000*1.85

A=120250

I=120250-65000

I=55250

The compound interest rate earns more by (55250-41600) =$13,650

To double the interest using simple interest calculation;

65000=65000*0.069*T

T=65000/4485

T=14.49years

To double the interest using compound rate calculation:

130000=65000(1+0.069)^T

(1+0.069)^T=130000/65000

1.069^T=2

T=In(2)/In(0.069)

T=10.39years

To quadruple your money using simple rate calculation:

195000=65000*0.069*T

T=195000/4485

T=43.48Years

To quadruple your money using compound rate calculation;

260000=65000(1+0.069)^T

1.069^T=4

T=In(4)/In(1.069)

T=20.78years