Question

A loan of $5500.00 was repaid together with interest of $1164.00. If interest was 6% compounded quarterly, for how many months was the loan taken out?

40.68 months
40.68 months ,

38.68 months
38.68 months ,

39.68 months
39.68 months ,

23 months

Answer 1

Loan = $5500

Interest = $1164

interest rate = 6% = 0.06

Compound interest formula:

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

A = final value = 5500 + 1164 = 6664

P = initial value = 5500

r = 0.06

n= compounding periods = 4

t = years:

6664 = 5500 (1 + 0.06/4 )^4 y

6664 = 5500 ( 1.015)^4y

6664/5500 = ( 1.015)^4y

1.21 = 1.015^4y

Ln 1.21 = Ln 1.015 ^4y

Ln 1.21 = 4y Ln 1.015

Ln 1.21 / Ln 1.015 = 4y

12.89 =4y

12.89/4 = y

y= 3.2234 years = 38.68 months

Answer:

38.68 motnhs