The answer is $7,980.98. Need step by step solution. payments at the end of e co

Question

The answer is $7,980.98. Need step by step solution. payments at the end of e computed using an annual effective ch er in a 5-ears. Theseakes an interest minal interest rate of 4.2% (2) The borrower in a $238,000 loan makes interest pa count rate of6.5%. Each time he makes an interest payment, t makes a deposit into a sinking fund earning a nominal interest convertible monthly. The amount of each sinking fund deposit is te of 4.2% three years and 2D in the remaining five years, and the sinkino fun the at the end of the eight years is equal to the loan amount. Find Dbalane the borrower also

Explanation / Answer

Solution: Calculation of effective semi-annual rate:

4.2% ÷ 12 = 0.35% (effective monthly) and [(1.0035)^6 - 1] = 2.118461% (effective semi-annually)

Since, the deposits are made at the end of every 6 months, the 1st deposit of 'D' will accumulate Interest 15 times before the end of 8 years, the 2nd deposit will accumulate Interest 14 times and so on until the 6th deposit, which is the last deposit of amount 'D' and which accumulates 10 times. Then the borrower deposit '2D' which accumulates 9 times, on until his last deposit of '2D' which accumulates no interest(it's at the end of the 8 years)

According to question;

D*{[(1.02118461)^16 - 1]÷(1.02118461-1)} + D*{[(1.02118461)^10 - 1]÷(1.02118461-1)} = 238000

After solving this equation we will get;

Therefore, D = $7,980.98

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