felipe needs to invest to help with his childs college fund. how much would he have to invest to have…

felipe needs to invest to help with his childs college fund. how much would he have to invest to have $97,200 after 14 years, assuming an interest rate of 2.27% compounded daily? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas. assume there are 365 days in each year.

felipe needs to invest to help with his childs college fund. how much would he have to invest to have $97,200 after 14 years, assuming an interest rate of 2.27% compounded daily? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas. assume there are 365 days in each year.

Answer

Explanation:

Step1: Recall the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (A) is the final amount, (P) is the principal (initial investment), (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years.

We are given that (A=$97200), (r = 2.27%=0.0227), (n = 365) (compounded daily), and (t = 14) years. We need to solve for (P).

First, rewrite the formula for (P): (P=\frac{A}{(1 +\frac{r}{n})^{nt}})

Step2: Substitute the values into the formula

Substitute (A = 97200), (r=0.0227), (n = 365), and (t = 14) into the formula for (P):

[ \begin{align*} P&=\frac{97200}{(1+\frac{0.0227}{365})^{365\times14}}\ &=\frac{97200}{(1 + 0.0000621918)^{5110}}\ &=\frac{97200}{(1.0000621918)^{5110}} \end{align*} ]

Using a calculator, ((1.0000621918)^{5110}\approx1.3677)

Step3: Calculate (P)

[ P=\frac{97200}{1.3677}\approx71070 ]

Answer:

(71070)