A person invests 4500 dollars in a bank. The bank pays 4.5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 8200 dollars?

Answer: the person must leave the money for 13.4 years.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = $8200

P = $4500

r = 4.5% = 4.5/100 = 0.045

n = 12 because it was compounded 12 times in a year.

Therefore,

8200 = 4500 (1 + 0.045/12) ^12 * t

8200/4500 = (1 + 0.00375) ^12t

1.8222 = (1.00375) ^12t

Taking log of both sides,

Log 1.8222 = 12t * log 1.00375

0.261 = 12t * 0.001626

0.261 = 0.019512t

t = 0.261/0.019512

t = 13.4 years