Investment Present Value
1. **Problem Statement:** You want to have 2.5 million after 5 years by investing a one-time amount now in a money market account with an annual interest rate of 5.8%. We need to find the present investment amount.
2. **Formula Used:** The future value $FV$ of a one-time investment $PV$ compounded annually at rate $r$ for $t$ years is given by:
$$FV = PV \times (1 + r)^t$$
3. **Rearranging to find $PV$:**
$$PV = \frac{FV}{(1 + r)^t}$$
4. **Substitute the values:**
- $FV = 2,500,000$
- $r = 0.058$
- $t = 5$
$$PV = \frac{2,500,000}{(1 + 0.058)^5}$$
5. **Calculate the denominator:**
$$ (1 + 0.058)^5 = 1.058^5 $$
Calculate stepwise:
$$1.058^2 = 1.119364$$
$$1.058^3 = 1.119364 \times 1.058 = 1.184$$
$$1.058^4 = 1.184 \times 1.058 = 1.253$$
$$1.058^5 = 1.253 \times 1.058 = 1.326$$
6. **Calculate $PV$:**
$$PV = \frac{2,500,000}{1.326} \approx 1,885,350$$
7. **Interpretation:** You need to invest approximately 1,885,350 now to have 2.5 million in 5 years at 5.8% annual interest.