A $4,000 payment has to be made 3 years from now and another $6,000 payment 5 years from now. Using the financial functions on the calculator, determine what lump sum payment 40 months from now will be equivalent to these two payments if interest is 5.2% compounded quarterly.
A) $11,654.38
B) $11,253.35
C) $11,053.35
D) $12,454.35
E) $12,675.35

Question

Quizplus · Accepted Answer

To calculate the equivalent lump sum payment, we need to find the present value of both payments at 40 months from now using the given interest rate and then add them up. Then, we can find the equivalent lump sum payment that will be made at 40 months from now.

Present value of $4,000 payment after 40 months:
n = 20 (since interest is compounded quarterly)
r = 5.2%/4 = 1.3% (quarterly rate)
PV = FV/(1+r)^n = 4,000/(1+0.013)^20 = $2,984.46

Present value of $6,000 payment after 40 months:
n = 20 (since interest is compounded quarterly)
r = 5.2%/4 = 1.3% (quarterly rate)
PV = FV/(1+r)^n = 6,000/(1+0.013)^20 = $4,474.70

Equivalent lump sum payment after 40 months:
PV = 2,984.46 + 4,474.70 = $7,459.16

Finally, to find the lump sum payment that will be made at 40 months from now, we need to find the future value of $7,459.16 after 40 months:

n = 10 (since interest is compounded quarterly)
r = 5.2%/4 = 1.3% (quarterly rate)
FV = PV*(1+r)^n = 7,459.16*(1+0.013)^10 = $11,053.35

Therefore, the correct answer is C) $11,053.35.

A $4,000 Payment Has to Be Made 3 Years from Now