to help with his childs college fund, ryan needs to invest. assuming an interest rate of 2.16% compounded…

to help with his childs college fund, ryan needs to invest. assuming an interest rate of 2.16% compounded annually, how much would he have to invest to have $78,900 after 12 years? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

to help with his childs college fund, ryan needs to invest. assuming an interest rate of 2.16% compounded annually, how much would he have to invest to have $78,900 after 12 years? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Recall the compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the future value, $P$ is the principal (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We are given $A=$78900$, $r = 0.0216$, and $t = 12$. We need to solve for $P$.

Step2: Rearrange the formula to solve for $P$

From $A = P(1 + r)^t$, we can get $P=\frac{A}{(1 + r)^t}$. Substitute the given values: $A = 78900$, $r=0.0216$, and $t = 12$. So, $P=\frac{78900}{(1 + 0.0216)^{12}}$.

Step3: Calculate the denominator

First, calculate $(1 + 0.0216)^{12}$. Using the formula $a^n=e^{n\ln(a)}$ (or a calculator's power function), $(1.0216)^{12}\approx1.29177$.

Step4: Calculate $P$

Now, $P=\frac{78900}{1.29177}\approx61080$.

Answer:

$61080$