A person invests 4500 dollars in a bank. The bank pays 6.75% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 6300 dollars?

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,

P = 4500

A = 6300

r = 6.75% = 6.75/100 = 0.0675

n = 2 because it was compounded 2 times in a year.

Therefore,.

6300 = 4500 (1 + 0.0675/2) ^2t

6300/4500 = (1 + 0.03375) ^2t

1.4 = 1.03375^2t

Taking log of both sides of the equation, it becomes

Log 1.4 = 2t log 1.03375

0.1461 = 2t * 0.0144 = 0.0288t

t = 0.1461/0.0288

t = 5.1 years.