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 (i.e. at time t = 0 years), and the second payment is due at the end of the first year (i.e. at time f = 1 year). Calculate X. Give your answer rounded to the nearest whole number.

Explanation / Answer

All Amounts in $ To calculate X, we first need to have the Present Values of both the loans First Loan Effective Interest Rate = 5.063% Second Loan Effective Interest Rate = 5.095% The Present Value of the First Loan is $ 10,622.30 The Present Value of the Second Loan is $ 17,272.52 Total Present Value $ 27,984.82 This value is to be repaid by two equal instalments of X with interest @ 5% Thus, 2X + 5% * X * 2 = $ 27,984.82 Hence, 2X + 0.1X = $ 27,984.82 or X = $ 27,984.82 / 2.1 = 13326 $

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