Question

An investment currently costs $28,000. If the current inflation rate is 6% and the effective annual return on investment is 10%, approximately how long will it take for the investment's future value to reach $40,000?

Answer 1

Answer:

time require is 2.3 years

Explanation:

given data

currently costs = $28,000

inflation rate = 6%

effective annual return = 10%

future value = $40,000

solution

first we get here interest rate that is

interest rate = annual return investment + inflation rate + ( annual return × inflation rate )   .......................1

put here value and we get

interest rate = 0.10 + 0.06 + ( 0.10 × 0.06 )

interest rate = 0.166

and now we get here present value that is express as

future value = present value × $(1+r)^{t}$     .....................1

put here value and we get

present value = $\frac{40000}{(1+0.166)^t}$    

28000 = $\frac{40000}{(1+0.166)^t}$

0.7 = $(1.166)^{-t}$

take log both side we get

log( 0.7) = -t log (1.166)

solve it we get

t = 2.3  year

so time require is 2.3 years