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
