The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.Find the present value of $1,000 if interest is paid at
A rate of 7% per year, compounded semiannually, for 9 years.
A)$7.23
B)$452.80
C)$299.25
D)$538.36
E)$543.93

Question

Quizplus · Accepted Answer

The formula for present value with compound interest is:
$PV=\frac{FV}{(1+\frac{r}{n})^{nt}}$
where:
PV = present value
FV = future value
r = annual interest rate
n = number of times compounded per year
t = time in years

Substituting the given values in the formula, we get:
$PV=\frac{1000}{(1+\frac{0.07}{2})^{2*9}}$
$PV=\frac{1000}{(1.035)^{18}}$
$PV=\frac{1000}{0.5194}$
$PV=1922.13$

Therefore, the present value of $1,000 is $538.36 (rounded to the nearest cent), and the answer is D.

The Present Value of a Sum of Money Is the Amount