Question

Your parents are giving you $210 a month for four years while you are in college. At an interest rate of .49 percent per month, what are these payments worth to you when you first start college?

Answer 1

Answer:

These payments will be worth $11,332.94.

Step-by-step explanation:

We can calculate this as an annuity but with monthly periods and monthly interest rates.

Then, we have:

C = cash flow per period = $210

n = number of payments = 48

i = interest rate = 0.49% = 0.0049

Then, we can calculate the future value of this stream of deposits as:

$FV=C\left[\dfrac{(1+i)^n-1}{i}\right]\\\\\\FV=210\left[\dfrac{(1.0049)^{48}-1}{0.0049}\right]=210\left[\dfrac{1.2644-1}{0.0049}\right]=210\left[\dfrac{0.2644}{0.0049}\right]\\\\\\FV=210\cdot 53.966\\\\\\FV=11332.94$