Question

How much should a new graduate pay in 10 equal annual payments, starting 2 years from now, in order to repay a $30,000 loan he has received today? The interest rate is 6% per year. (Note: the first payment is made at the end of year 2, so the cash flows are: at initial time = 0; at the end of the first year = 0; at the end of the second year = C, ... , at the end of the year 10 = C. Here "C" denotes the yearly payments. You need to find "C").

Answer 1

Answer:

each payment will for 4,320.60 dollars

Explanation:

First, we will calculate the future value of the 30,000 two years from now

then we calcaualtethe annuity present value of this to know the student payment

timeline:

<---//----/-/-/-/-/-/-/-/-/-/-/->

loan    student payments

the loan futre value will be:

30,000 x 1.06^{2} = 33708

Now we calculate an annuity-due which 10 payment being made at 6% discount rate

This will be an annuity-due because today we are receiving the loan and in excatly 2 years form now we will start the payment so it will be at the beginning of the period

Annuity-due formula

$PV \div \frac{1-(1+r)^{-time} }{rate} (1+r) = PTM$

PV  $33,708.00

time 10 years

rate          0.06 discount rate

$33,708 \times \frac{1-(1+0.06)^{-10} }{0.06} (1+0.06)= PTM$

PTM = $ 4,320.601