Question

You expect to receive $19,000 at graduation in two years. You plan on investing it at 11 percent until you have $92,000. How long will you wait from now?

a. 15.11 years

b. 13.11 years

c. 19.17 years/

d. 17.11 years

e. 18.83 years

Answer 1

Given,

Value in 2 years = $19000

Interest rate (r) = 11% or 0.11

Future value = $92000

Solution :-

Let number of years be 'n'

Future value = value in 2 years x (1 + r)ⁿ

$92000 = $19000 x (1 + 0.11)ⁿ

$92000/$19000 = (1.11)ⁿ

4.84210526315 = (1.11)ⁿ

Taking 'Log' both sides,

Log(4.84210526315) = Log(1.11)ⁿ

Log(4.84210526315) = n.Log(1.11)

1.5773495979 = n.(0.10436001532)

1.5773495979/0.10436001532 = n

15.11 = n

Investment period would be 15.11 years.

First 2 years from now would not be the investment period.

Thus,

Total number of years from now = 15.11 years + 2 years = 17.11 years

Option 'd' is correct.