Question

if an investor advisor promises to double your money in 7 years, he's promising an annual return of approximately ? %. If, however, you earn an actual annual return of only 5.5%, it would take approximately ? year to double your mone.

A. 9.72; 7.64

B. 7.64; 9.72

C. 10.3; 13.1

D. 13.1; 10.3

Please explain why. Thank you.

Answer 1

Option (C) is correct

Here we will use the following formula to calculate the required amounts.

FV = PV (1+R%)ⁿ

where, FV = Future value, PV = Present value, R is the rate of interest and n is the time period.

In the first case, let us assume that we invest $500 that will be double in 7 years. So, our FV will be $1000, PV will be $500, n will be 7 years and R has to be find out.So, putting these values into the above formula, we get,

1000 = 500 (1+ R%)⁷

2 = (1+R%)⁷

2^1/7= 1 +R%

1.10408 = 1+R%

R% = 1.1030 - 1

R% = 0.1030

R = 10.30%

In the second case, let us assume that we invest $500 that will be double in 7 years. So, our FV will be $1000, PV will be $500, R is 5.5% and n has to be find out.So, putting these values into the above formula, we get,

1000 = 500 (1+ 5.5%)ⁿ

2 = (1.055)ⁿ

(1.055)^13.1= (1.055)ⁿ

n= 13.1