Question

1.

What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two years later?

Group of answer choices

12%

25%

6%

18%

4%


2.

At an effective interest rate of 12%, a single sum invested today will double itself in approximately:

Group of answer choices

8 years.

12 years.

6 years.

insufficient data to determine answer.

Answer 1

1) Present Value (PV) = 1000

Future Value (FV) = 1254.7

Rate of return (r) = ?

No.of years (n) = 2 years

FV = PV*(1+r)^n

1254.7 = 1000*(1+r)^2

1254.7/1000 = (1+r)^2

1.2547 = (1+r)^2

(1+r) = square root of 1.2547

1+r = 1.12

r = 1.12-1

r = 0.12 or 12%

Rate of Return = 12%

2) Amount invested today let us assume 'x'

Present Value (PV) = x

Amount will become double in the future let it be '2x'

Future value (FV) = 2x

Rate of interest (r) = 12%

FV = PV*(1+r)^n

2x = x*(1+0.12)^n

2x/x = (1.12)^n

2 = (1.12)^n

log 2 = n log 1.12

n = log 2 / log 1.12

n = 0.3010/0.0492

n = 6 years