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: 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