Question

What amount must be invested for 33 months at \( 5 \% \) compounded monthly to reach a maturity value of \( \$ 6,800 \) ? (Round dollar values to two decimal places.) \[ \begin{array}{l} N= \\ P V= \\

Answer 1

To determine how much needs to be invested at a 5% annual interest rate compounded monthly for 33 months to reach a maturity value of $6,800, we use the compound interest formula to calculate the present value.

Step-by-step explanation:

The question involves finding the initial investment amount (PV for Present Value) that must be made at a 5% annual interest rate compounded monthly to achieve a future value (FV) of $6,800 after 33 months. We use the compound interest formula FV = PV * (1 + r/n)^(nt), where:

1. FV is the future value,
2. PV is the present value (the initial investment we want to calculate),
3. r is the annual interest rate (decimal),
4. n is the number of times interest is compounded per year,
5. t is the time the money is invested for in years.

In this case, r is 0.05 (5%), n is 12 (as interest is compounded monthly), and t is 33/12 years (since 33 months is 33/12 years).

Substituting the known values into the formula and solving for PV, we calculate the initial investment required to reach the $6,800 after 33 months.