Question

Consider the following scenarios:

i - an investor deposited $1,000 ten years ago in an investment account and earned a compound annual interest of 5% yielding a balance of $1,628.89 today.

ii - an investor will deposit $1,000 five years from now in an investment account which is expected to earn a compound interest of 5% and yield a balance of $1,628.89 over a ten year period. The money will be used for a gift to the investor's child that was born today and will be 15 years old when the ten-year investment period ends.

Under which of the above scenarios could the $1,628.89 amount be considered the future value of $1,000?

Group of answer choices

Under scenario (ii) only because that is the only scenario where the amount will be reached at a future date

Under neither scenario because in neither case the initial deposit is made today

Under both scenarios because $1,628.89 represents a future value after a ten year period.

Answer 1

Given Deposit of $ 1000 is made ten years ago in scenario 1

Deposit of $ 1000 will be made now for ten year period

In both the cases Compound annual interest rate given is 5%

Future value of deposit = Present value*[(1+rate of interest)^no. of years of deposit]

i.e., 1000*[(1+0.05)^10] = $ 1628.89

Therefore future value of deposit of $ 1000 for 10 years @ 5% compound interest per annum

is $ 1628.89

In both the scenario's of 1&2 the above future value calculation holds good

Therefore the answer will be

Under both scenarios because $1,628.89 represents a future value after a ten year period.

note:

In scenario 2, I can't understand how a child born now will be 15 years old when

ten year investment matures.

But, Since the question is about Future value calculation I didn't consider it.