Question

7) You will receive $4,000 at graduation 3 years from now. You plan on investing this money at 5 percent annual interest until you have accumulated $50,000. How many years from today will it be when this occurs? (Provide an approximation using the tables or an exact number if using Excel)

Answer 1

We can solve this problem by using the formula of compounding of an amount and finding the value of 'n' (discussed later) and adding 3 years. See the solution below:

A=P(1+r)ⁿ

^{where A= compounded amount}

^{P= Principal}

^{r= rate of interest}

^{n= number of compounding period(years in present case)}

50000=4000(1.05)ⁿ

1.05ⁿ=50000/4000

log natural(1.05)ⁿ=log natural12.5

n*ln1.05=ln12.5

n= ln12.5/ln1.05

=51.76716839

Means 4000 to be received 3 years from now shall take 51.76716839 years to become 50000.

And from now it will take 54.76716839 (i.e. 51.76716839+3) years to become $50000.

I hope you understood the concept.

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