You are given two loans, with each loan to be repaid by a single payment in the

Question

You are given two loans, with each loan to be repaid by a single payment in the future. Each payment includes both principal and interest. The first loan is repaid by a 3000 payment at the end of four years. The interest is accrued at an annual nominal rate of discount equal to 5% compounded semiannually The second loan is repaid by a 4000 payment at the end of five years. The interest is accrued at an annual nominal rate of interest equal to 5% compounded quarterly These two loans are to be consolidated. The consolidated loan is to be repaid by two equal installments of X, with interest accruing at an annual effective rate of 5%. The first payment is due immediately (ie, at time t = 0 years), and the second payment is due at the end of the first year (ie, at time t-1 year) Calculate X. Give your answer rounded to the nearest whole number

Explanation / Answer

Rounding off X = 2859.

1st Loan PV of loan 3000/(1+5%/2)^8 2462.24 2nd Loan PV of loan 4000/(1+5%/4)^20 3120.03 Total Loan Value 5582.27 (5582.27-X)*1.05 = X X = $2,859.21

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