Question

Please post with mathematical formulas please, no an excel sheet

2. The lender of a loan of 175000 receives interest payments at the end of each year for 25 years at an effective annual interest rate of i, and in addi tion, will receive a lump-sum repayment of the principal along with the 25th interest payment. The borrower will pay the annual interest to the lender and accumulate the 175000 by making 25 level annual deposits at the end of each year to a sinking fund. The borrower's total amount paid over the course of the loan is 339396 The effective annual interest rate on the sinking fund is 2.5°/o for the first seven years and 3°/o thereafter. Find the annual deposit in the sinking fund and the net interest paid by the borrower in the 8th total payment.

Answer 1

The total amount paid by the borrower is $339,396. Out of this amount, the principal equals $175,000 Now the value of the sinking fund payment would be such that the future value of 25 such payments is equal to $175,000 at the end of year 25. This can be calculated using the formula to calculate the future value of an annuity, which is given below: [1+r-1 Future value =C Here The equal annual payment is denoted by C The annual interest rate is r The total number of payments is n. According to the question the following relationship would hold: (1+2.5%- (1+3%)--1 (25-7) $175,000 C x(1+3%* C 2.5% 3% $175,000 C(12.84899461+23.41443537) $175,000 36.26342998 = $4,825.80 In the above formula, the equal payment for the first 7 years is compounded at an interest rate of 2.5%, and then this value is further compounded at 3% to get its value at the end of year 25. The future value of the same payment, starting from year 8 is also calculated and the final of the sum of the two is equal to the total principal payment This suggests that the sinking fund payment is equal to $4,825.80 The total amount of interest being paid in the 25-year period is equal to $164,396 ($339,396-$175,000). This suggests that the interest paid per year can be calculated as follows: Total interest paid Number of years Interest paid per year = $164,396 25 - $6,575.84 Therefore, the annual interest payment made in this arrangement is $6,575.84