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

question 4

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. $A = \$ 10,000 , r = 6 \% , t = 5 \text { years } , n = 4$

• A) \(P \approx 6424.70\)
• B) \(P \approx 3424.70\)
• C) \(P \approx 4424.70\)
• D) \(P \approx 7424.70\)
• E) \(P \approx 5424.70\)

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Definitions:

Face Value

The nominal or dollar value stated on a security or financial instrument, such as a bond or stock.

Real Rate

The interest rate adjusted for inflation, reflecting the true cost of borrowing.

Inflation Rate

The rate that reflects how the overall prices of services and goods escalate, causing a reduction in the capacity to purchase.

Treasury Bill

A short-term government security with a maturity of less than one year, sold at a discount to face value to provide a return to the holder upon maturity.