The Present Value of Money Is the Principal $P$ You Need to Invest Today So That It Will Grow

question 50

Multiple Choice

The present value of money is the principal $P$ you need to invest today so that it will grow to an amount $A$ at the end of specified time. The present value formula $P = A \left( 1 + \frac { r } { n } \right) ^ { - n t }$ is obtained by solving the compound interest formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ for $P$ . Recall that $t$ is the number of years, $r$ is the interest rate per year, and $n$ is the number of compoundings per year. find the present value of amount $A$ invested at rate $r$ for $t$ years, compounded $n$ times per year. $A = \$ 1,000,000 , r = 8 \% , t = 20 \text { years }, n = 2$

• A) \(P \approx \$ 108,289.04\)
• B) \(P \approx \$ 208,289.04\)
• C) \(P \approx \$ 308,289.04\)
• D) \(P \approx \$ 20,289.04\)
• E) \(P \approx \$ 1008,289.04\)

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