Question

A person invests 5000 dollars in a bank. The bank pays 4% interest compounded

annually. To the nearest tenth of a year, how long must the person leave the money

in the bank until it reaches 8200 dollars?

A= P(1+ r over n)^nt

Answer 1

Answer: 12.6 years

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:  

A = P (1 + r/n) nt  

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r = Nominal Interest Rate (decimal form, 4/100= 0.04)

n= number of compounding periods in each year (1)

t = years

Replacing with the values given  

8200= 5000(1+ 0.04/1)^1(t)

Solving for t

8200 =5000 (1.04)^t

8200/5000 =(1.04)^t

1.64 =(1.04)^t

log 1.64 =log (1.04)^t

log 1.64 = t log (1.04)

log 1.64/ log (1.04) =t

t = 12.6 years