jericho wants to start saving to purchase a house. his goal is to save $92,400 in 17 years. what amount…

jericho wants to start saving to purchase a house. his goal is to save $92,400 in 17 years. what amount should he deposit into an account that pays 2.92% interest compounded daily, in order for his money to grow to the desired amount? round your answer to dollars and cents. include dollar symbol $ and comma if necessary.

jericho wants to start saving to purchase a house. his goal is to save $92,400 in 17 years. what amount should he deposit into an account that pays 2.92% interest compounded daily, in order for his money to grow to the desired amount? round your answer to dollars and cents. include dollar symbol $ and comma if necessary.

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (A) is the final amount ((A = 92400)), (P) is the principal amount (the initial deposit we want to find), (r) is the annual interest rate (as a decimal, (r=0.0292)), (n) is the number of times interest is compounded per year ((n = 365) for daily compounding), and (t) is the number of years ((t = 17)). We need to solve for (P), so we can rewrite the formula as (P=\frac{A}{(1 +\frac{r}{n})^{nt}}).

Step2: Substitute the values into the formula

Substitute (A = 92400), (r = 0.0292), (n=365), and (t = 17) into the formula: [ \begin{align*} P&=\frac{92400}{(1+\frac{0.0292}{365})^{365\times17}}\ &=\frac{92400}{(1 + 0.00008)^{6205}}\ &=\frac{92400}{(1.00008)^{6205}} \end{align*} ] First, calculate ((1.00008)^{6205}). Using a calculator, ((1.00008)^{6205}\approx1.6097).

Step3: Calculate the value of (P)

Then (P=\frac{92400}{1.6097}\approx57401.99)

Answer:

($57,402.00)