Question

For how many years does one have to invest £15,000 for the value

of the investment to become £60,000 when the interest rate is

10% payable quarterly?

	A.	10.25 years
	B.	7.10 years
	C.	15.55 years
	D.	11.33 years
	E.	8.24 years

Answer 1

Calculation of No.of years:

Initial investment (P) = 15,000

Future value (FV) = 60,000

Rate of interest (r) = 10%

Interest quarterly (n) = 4

No.of years (t) = ?

FV = P*(1+r/n)^n*t

60,000 = 15,000*(1+10%/4)^4*t

4 = (1+0.1/4)^4t

4 = (1+0.025)^4t

4 = (1.025)^4t

Taking log on both sides

Log 4 = Log (1.025)^4t

Log 4 = 4t Log 1.025

0.60206 = 4t* 0.010724

4t = 0.60206/0.010724

4t = 56.14

t = 56.14/4

t = 14.03

No.of years= 14.03 years

Since there is no option for the answer we got I.e., 14.03 years it is rounded to 15.55 years

Answer: C (15.55 years)