Question

A debt of $3500 due in four years and $5000 due in six years is to be repaid by a single payment of $1500 now and three equal payments that are due each consecutive year from now. If the interest rate is 7% compounded annually, how much are each of the equal payments?

Answer 1

Answer:

$1715.44

Step-by-step explanation:

The formula to calculate the present value is;

PV = S(1 + r)^(-n)

Where;

S is the current debt

r is the interest rate

n is the amount of years which the debt is due.

Thus, for the debt of $3500 & $5000, we have total debt value as;

PV = (3500(1 + 0.07)^(-4)) + (5000(1 + 0.07)^(-6))

PV_debt = $6001.84

Now,let's find total PV of the payments that will be made since a single payment of $1500 now and three equal payments that are due each consecutive year from now annually;

PV_payments = 1500 + x(1 + 0.07)^(-1)) + x(1 + 0.07)^(-2)) + x(1 + 0.07)^(-3))

Where x is the value of each of the equal payments.

Thus, expanding we have;

PV_payments = 1500 + x(1.07)^(-1)) + x(1.07)^(-2)) + x(1.07)^(-3))

>> PV_payments = 1500 + x((1.07)^(-1)) + (1.07)^(-2)) + (1.07)^(-3))

Solving the bracket we have;

PV_payments = 1500 + 2.6243x

To find the value of each equal payments, we will equate PV_debt to PV_payments to get;

6001.84 = 1500 + 2.6243x

Thus;

2.6243x = 6001.84 - 1500

2.6243x = 4501.84

x = 4501.84/2.6243

x = $1715.44