Mr. Smith borrows $8,000 from a bank that charges interest at 6% compounded mont

Question

Mr. Smith borrows $8,000 from a bank that charges interest at 6% compounded monthly. Mr. Smith has to pay the money back with six equal payments. However, the first payment is to be made immediately on receipt of the $8000. Successive payments are spcaed six-months part; that is, the loan repayments are made semi-annually.

a) Determine the size of the equal semi-annual payment.

b) At the time of the fourth payment, suppose Mr. Smith decides to pay off the loan with one lump sum payment. How much should be paid? Include the fourth payment.

Explanation / Answer

Interest= 6% p.a compounded monthly Hence, interest per month= 6%/12= 0.5% a Let the equal instalments be X 8000= [X]+ [X/(1.005)^6]+[X/(1.005)^12]+[X/(1.005)^18]+[X/(1.005)^24]+[X/(1.005)^30] 8000= [X]+ [0.971X]+[0.942X]+[0.914X]+[0.887X]+[0.861X] 8000= 5.575X Thus, X= 1434.98= 1435 (approx) b Sum due at the time of 4th payment= 8000*(1.005^24)= 8000*1.13= 9040 Less: Instalments paid(1435*4)= 5740 Hence, the amount required to clear the loan= 9040-5740= 3300

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.