A $4,000 obligation is to be repaid by three payments. The first payment is now, the second is 18 months from now, and the final payment is in 24 months. In addition the second payment will be half the amount of the first, while the third payment will be twice as much as the first. Interest is 4.8% compounded quarterly. Using the financial functions on the calculator, determine the size of each payment.
A) Payment #1 = $1,173.83; Payment #2 = $586.92; Payment #3 = $2,347.66
B) Payment #1 = $500; Payment #2 = $250; Payment #3 = $1,000
C) Payment #1 = $2520.50; Payment #2 = $1,260.25; Payment #3 = $5,041
D) Payment #1 = $3,300.75; Payment #2 = $1,650.38; Payment #3 = $6,601.50
E) Payment #1 = $875.50; Payment #2 = $437.75; Payment #3 = $1,751

Question

Quizplus · Accepted Answer

Using the financial functions on the calculator, we can use the PMT (payment) function to solve for the payments.

For Payment #2:
PMT = ? (what we want to solve)
N = 6 (18 months = 6 quarters)
PV = $4,000
FV = 0 
I/Y = 4.8%/4 = 1.2% (interest rate per quarter)
Solve for PMT: 
PMT = $1,173.83

For Payment #3:
PMT = ? (what we want to solve)
N = 8 (24 months = 8 quarters)
PV = $4,000 - $1,173.83 - $586.92 = $2,239.25 (subtracting payments already made)
FV = 0 
I/Y = 4.8%/4 = 1.2% (interest rate per quarter)
Solve for PMT: 
PMT = $2,347.66

For Payment #1:
Using the information that Payment #2 will be half the amount of Payment #1, we know Payment #2 will be $1,173.83/2 = $586.92. Using the information that Payment #3 will be twice as much as Payment #1, we know Payment #3 will be $1,173.83 x 2 = $2,347.66. Therefore, Payment #1 will be the total amount owed minus payments 2 and 3: 
Payment #1 = $4,000 - $1,173.83 - $2,347.66 = $478.51

So the final answer is A.

A $4,000 Obligation Is to Be Repaid by Three Payments