Question

A debt can be repaid by payments of $5125.00 today, $4770.00 in two years and $5600.00 in five years. What single payment would settle the debt three years from now if money is worth 9.88% p.a. compounded quarterly?

Answer 1

To Calculate the amount that has to be paid in single installment from 3 years Now.

We will set the Number of period = 3 and bring these value at that period of time.

Interest rate = 9.88%

Interest rate per quarter = 9.88%/4

= 2.47%

Effective rate = [(1 + Rate per period)^Number of compounding] - 1

= ( 1+ 2.47%)^ 4 - 1

= 1.0247^4 -1

= 0.1025211 or 10.252%

Value of $5125 from 3 years Now

= Present Value * ( 1 + Interest rate ) ^ Number of period
= 5125 * ( 1+10.252%)^3

= 6868.363

Value of 4770 at 3 years

= Present Value * ( 1 + Interest rate ) ^ Number of period

= 4770 * ( 1 + 10.252%) ^ (3-2)

= 4770 * 1.10252

= 5259.0204

Value of 5600 In 3 years

Present Value = Future Value / ( 1 + rate ) ^ Number of period

= 5600 / ( 1 + 10.252%)^ ( 5 - 3)

= 5600 / ( 1.10252)^2

= 4606.96

So, The Single payment that will settle the debt is Sum of all the payments = 5259.0204+ 4606.96 + 6868.363

= 16734.3434