The parents of a student at an expensive private school are experiencing financi

Question

The parents of a student at an expensive private school are experiencing financial difficulties. They enter an agreement with the school to pay the annual school fees in weekly installments. Instead of paying $8600 immediately they will make the first of 46 weekly installments at the end of six weeks. If the school charges interest of 8% per annum, compounded weekly, for the whole period until the debt is repaid, how much will each payment be?

(b) The parents decide that because of continuing business problems they also need to take out a loan of $100,000 to be repaid over 10 years, using their house as security.

(i) Initially the interest charged on the loan is 9% per annum, compounded monthly. Payments are made at the end of each month. What is the amount of the payment?

(In your calculations for Part (b) use interest rates correct to four decimal places.)

Explanation / Answer

A. Given Information

Amount at present =$8600

Interest rate 8% and since it will compunded weekly i.e 52 weeks in year , Per week Interest rate will be =0.08/52 =0.0015%

N =46 Week in which amount will be repaid but will start 6 weeks from now.

First we need to calculate the value of 8600 at six weeks fromnow.

= Amount *(1+r)^n

= 8600*(1.0015)^6

= $8679.69

Now we need to calculate the weekly installment amount starting 6 weeks from now

= Present value/(((1-(1/(1+r)^n))/r)

= 8679.69/(((1-(1/1.0015^46))/0.0015)

= 8679.69/((1-(1/1.0733)/0.0015)

= 8679.69/((1-0.9317)/0.0015)

= 8679.69/(0.0683/0.0015)

=$195.5894

B. Given Information

Amount need to be repaid = $100000

Interest rate = 9%, since it will compunded monthly i.e 12 months in year , Per month Interest rate will be =0.09/12 =0.0075%

N= 10*12= 120 since it iscompunded monthly

Now we need to calculate the monthly installment amount

= Present value/(((1-(1/(1+r)^n))/r)

= 100000/(((1-(1/1.0075^120))/0.0075)

= 100000/((1-(1/2.4514)/0.0075)

= 100000/((1-0.4079)/0.0075)

= 100000/(0.5921/0.0075)

=$1266.7577

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