Question

Jaylin makes a 25-year loan of 150,000 to Susan. Susan needs to repay this loan by level end of year payments R. Jaylin will replace her capital via a savings account which offers annual effective interest rate 6% and earn an APY of 4%. Find R.

Answer 1

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Answer:

We are given with the a 25-year loan of $150,000 with yearly payments of R

In this case, we are given with an Annual effective interest rate to be paid as 6%, but we are not interested in the 4% APY because it is the part of her earnings which will not account for the payments that she is supposed to make. Rather, it is the only 6% that matters when the payments have to be paid.

We now calculate the discount factor for the monthly payments to be made using the formula:

=> Discount Factor= {[(1 + r)ⁿ] - 1} / [i(1 + r)ⁿ]

where r is the rate = 6% and n is the number of yearly payments to be made = 25

=> Discount factor = {[1.06]²⁵ -1}/[0.06(1.06)²⁵]

=> Discount factor = 3.2918/0.2575 = 12.807

We now divide the mortgage amount by the discount factor to get the yearly payments

=> Yearly payments = $150,000/12.807 = $ 11,712.2