Two payments of $49 000 each must be made 3 year and 5 year from now. If money can earn 4.9% compounded monthly, what single payment 5 years from now would be equivalent to the two scheduled payments?
A) $98 117
B) $98 000
C) $103 034
D) $105 742
E) $101 177

Question

Quizplus · Accepted Answer

First, we need to find the present value of the two scheduled payments using the compound interest formula:

PV = C/(1 + r/n)^(nt)

where 
C = payment amount 
r = annual interest rate 
n = number of times interest is compounded per year 
t = time in years

For the first payment of $49 000 due in 3 years:

PV1 = 49 000/(1 + 0.049/12)^(12*3) = $40 846.96

For the second payment of $49 000 due in 5 years:

PV2 = 49 000/(1 + 0.049/12)^(12*5) = $39 080.74

Total present value of the two payments is:

PV = PV1 + PV2 = $79 927.70

Next, we need to find the future value of this amount in 5 years using the compound interest formula:

FV = PV*(1 + r/n)^(nt)

where 
FV = future value 
PV = present value 
r = annual interest rate 
n = number of times interest is compounded per year 
t = time in years

FV = 79 927.70*(1 + 0.049/12)^(12*5) = $103 033.79

Therefore, a single payment of $103 033.79 made 5 years from now would be equivalent to the two scheduled payments of $49 000 each. The closest option is C with an answer of $103 034.

Two Payments of $49 000 Each Must Be Made 3