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

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 $FV=2000(1+\frac{0.024}{4}{)}^{4\ast 5}$ .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 $FV=4000(1+\frac{0.024}{4}{)}^{4\ast 1.5}$ .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.