Question

A loan of 299,000 is initially repaid through 25 equal annual installments made at the end of each year at 4% interest effective annually. Immediately after the 9th payment, the loan is renegotiated as follows: (i) The borrower will make 32 equal semi-annual payments of X to repay the loan, with the first payment made four years from the date of renegotiation. (ii) The interest rate is changed to 8% compounded semi-annually. Calculate X. {use amortization formula}

          A loan of 299,000 is initially repaid through 25 equal annual installments made at the end of each year at 4% interest effective annually. Immediately after the 9th payment, the loan is renegotiated as follows:  (i) The borrower will make 32 equal semi-annual payments of  X to repay the loan, with the first payment made four years from the date of renegotiation.  (ii) The interest rate is changed to 8% compounded semi-annually.

Calculate X. 

{use amortization formula}

Added by Aki S.

Mathematics for Finance An Introduction to Financial Engineering

Marek Capinski 1st Edition

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Solved by Expert Oluwadamilola Ameobi

Step 1

The formula for the annual installment \( A \) is given by the annuity formula: \[ A = \frac{P \cdot i}{1 - (1 + i)^{-n}} \] where \( P = 299,000 \), \( i = 0.04 \), and \( n = 25 \). \[ A = \frac{299,000 \cdot 0.04}{1 - (1 + 0.04)^{-25}} \] Show more…

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A loan of 299,000 is initially repaid through 25 equal annual installments made at the end of each year at 4% interest effective annually. Immediately after the 9th payment, the loan is renegotiated as follows: (i) The borrower will make 32 equal semi-annual payments of X to repay the loan, with the first payment made four years from the date of renegotiation. (ii) The interest rate is changed to 8% compounded semi-annually. Calculate X. {use amortization formula}