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The present value of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. Approximately how much should be invested today in a savings account that earns
3% interest compounded annually in order to have
$500 in 2 years?
Choose 1 answer:
(A)
$530
(B)
$515
(c)
$485
(D)
$471

The present value of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. Approximately how much should be invested today in a savings account that earns $3 \%$ interest compounded annually in order to have $\$ 500$ in $2$ years? $\newline$ Choose $1$ answer: $\newline$ (A) $\$ 530$ $\newline$ (B) $\$ 515$ $\newline$ (C) $\$ 485$ $\newline$ (D) $\$ 471$

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Compound interest: word problems

Full solution

Q. The present value of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. Approximately how much should be invested today in a savings account that earns

3 \%

interest compounded annually in order to have

\$ 500

in

2

years?

\newline

Choose

1

answer:

\newline

(A)

\$ 530

\newline

(B)

\$ 515

\newline

(C)

\$ 485

\newline

(D)

\$ 471

Identify values: Identify the values of $FV$ (future value), $r$ (interest rate), $n$ (number of times the interest is compounded per year), and $t$ (time in years). $\newline$ Future Value ( $FV$ ) = $\$500$ $\newline$ Interest Rate ( $r$ ) = $3\%$ $\newline$ Number of times compounded annually ( $n$ ) = $1$ $\newline$ Time ( $t$ ) = $r$ $1$ years
Convert interest rate: Convert the interest rate from a percentage to a decimal. $\newline$ $r = 3\%$ $\newline$ $= \frac{3}{100} = 0.03$
Use present value formula: Use the formula for present value (PV), which is the inverse of the compound interest formula: $PV = \frac{FV}{(1 + \frac{r}{n})^{n*t}}$ . $\newline$ Substitute $\$500$ for FV, $0.03$ for r, $1$ for n, and $2$ for t. $\newline$ $PV = \frac{500}{(1 + \frac{0.03}{1})^{1*2}}$
Calculate present value: Calculate the present value. $\newline$ PV = $\frac{500}{(1 + \frac{0.03}{1})^{(1 \cdot 2)}}$ $\newline$ First, calculate the denominator: $(1 + \frac{0.03}{1})^{(1 \cdot 2)}$ $\newline$ = $(1 + 0.03)^{2}$ $\newline$ = $1.03^{2}$ $\newline$ = $1.0609$
Divide by denominator: Now, divide the future value by the calculated denominator to find the present value. $\newline$ $PV = \frac{500}{1.0609}$ $\newline$ $PV \approx 471.39$

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