A person invests 5000 dollars in a bank. The bank pays 6.5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 11300 dollars?

Answer: 13.6 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,

P = $5000

A = $11300

r = 6% = 6/100 = 0.06

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

Therefore,.

11300 = 5000 (1 + 0.06/12) ^12 * t

11300/5000 = (1 + 0.005) ^12t

2.26 = (1.005) ^12t

Taking log of both sides, it becomes

Log 2.26 = 12tlog 1.005

0.354 = 12t * 0.0022

0.354 = 0.0264t

t = 0.354/0.026

t = 13.6 years

19.38 Months, so 1.6 years

Step-by-step explanation:

6.5% compounded monthly is $325 a month (5,300*.065) so if you subtract 11,300-5,000 you get $6,300. You divide that by 325 and you get 19.38 (months) divide that by 12 months and you get 1.6 (years)