A $2,000 payment due 2 years ago and another $4,000 payment 18 months from now are to be replaced by a lump sum payment in 3 years. Using the financial functions on the calculator, determine the value of this payment if interest is at 2.4% compounded quarterly.
A) $6,000.34
B) $6,100.34
C) $6,200.34
D) $6,300.34
E) $6,400.34

Question

Quizplus · Accepted Answer

To find the lump sum payment that replaces both the past and future payments, we need to calculate the future value of both payments at the point in time 3 years from now, using the given interest rate of 2.4% compounded quarterly.1. For the $2,000 payment due 2 years ago, we're finding its value 5 years in the future (since it's 2 years ago from now, and we're calculating for 3 years from now, making it 5 years total). The formula for future value is $FV = PV(1 + \frac{r}{n})^{nt}$, where $PV$ is the present value, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the time in years. Plugging in the values, we get $FV = 2000(1 + \frac{0.024}{4})^{4*5}$.2. For the $4,000 payment due 18 months (or 1.5 years) from now, we're finding its value 1.5 years in the future (since we're calculating for 3 years from now). The formula is the same, so we get $FV = 4000(1 + \frac{0.024}{4})^{4*1.5}$.Using a financial calculator or software to compute these values and sum them gives us the total future value, which corresponds to option E, $6,400.34. This accounts for the compound interest accrued on both payments until the point 3 years from now.

A $2,000 Payment Due 2 Years Ago and Another $4,000