You will need at least $5,000 in four years and your friend says she can either loan you $5,000 all at once four years from now or she can deposit $1,200 in your savings account at the end of each year for the next four years. Your savings account earns 7% interest, compounded annually. Which option would be worth more to you four years from now, and how much more?

Question

Quizplus · Accepted Answer

To compare the two options, we need to find the future value of each, given the interest rate and compounding period.

Option 1: $5,000 in four years
FV = $5,000 x (1 + 0.07)^4
FV = $6,558.08

Option 2: $1,200 deposited at the end of each year for four years
FV = $1,200 x ((1 + 0.07)^4 - 1) / 0.07
FV = $5,229.48

Option 1 gives a higher future value of $6,558.08, but we need to subtract the principal amount borrowed, which leaves us with a net gain of $1,558.08.

Option 2 gives a lower future value of $5,229.48, but we don't need to subtract any principal amount borrowed. This means that the net gain is $5,229.48.

Therefore, option 2 - the annual deposits - is worth $3,671.40 more than option 1 - the lump sum in four years.

You Will Need at Least $5,000 in Four Years and Your