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Investment Present Value

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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.