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

Answer 2

It would take approximately 2.3 years for the future investment to reach 40000.

The present value = 28000

i = the rate of inflation = 6% = 0.06

f = effective return = 10% = 0.10

F = 40000

d = i+f+if

This is the adjusted rate of inflation

d= 0.06+0.1+0.06*0.1

= 0.166

$P = F(1+i)^-^n$

When we insert the values we would have:

$28000=40000(1+0.166)^-^n\\\\28000 = 40000(1.166)^-^n$

divide through by 40000

$\frac{28000}{40000} =1.166^-^n\\\\0.7 = 1.166^-^n$

Take the log of both sides

log0.7 = -nlog1.166

-0.15 = -n0.0166

divide through by 0.0166

n = 0.15/0.066

n = 2.27

Approximately 2.3 years

Therefore it would take approximately 2.3 years for the future investment to reach 40000.

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