Question

If your investment doubles in 6​ 3/4 years, what approximate annual rate of return would you have​ earned? If you could earn an annual rate of​ 7.50%, approximately how long would it take for your investment to​ double?

A. ​9.60%; 10.67 years

B. ​13.50%; 9.20 years

C. ​9.20%; 13.50 years

D. ​10.67%; 9.60 years

answer is NOT 10.81 and 9.58 !

Answer 1

A	B	C	D	E	F	G	H	I	J
2
3		a)
4
5		Let n be the number of years amount P is invested at rate APR at compounding frequency f, then
6		Future value (FV) can be calculated as follows:
7		FV = P*(1+ APR/f)n
8
9		In case of investment is doubled then
10		FV = 2P
11
12		Then,
13		2P = P*(1+ APR/f)n
14		or
15		2 = (1+ APR/f)n
16		or
17		APR	=(21/n-1)*f
18
19		Given
20		f	1	(Annual Compounding)
21		n	6.75
22
23		APR	=(21/n-1)*f
24			10.81%	=((2^(1/D21))-1)*D20
25
26		Hence APR is	10.81%
27
28
29		Calculation of time required to double the investment:
30
31		As derived above equation for doubling of investment is
32		2 = (1+ APR/f)n
33		or
34		n	=ln(2) / ln(1+APR/f)
35
36		Given
37		f	1	(Annual Compounding)
		APR	7.50%
39
40		n	=ln(2) / ln(1+APR/f)
41			9.58	=LN(2) / LN(1+D38/D37)
42
43		Hence Number of Years is	9.58
44
45		Thus the option (D) is approximately correct
46