How much must you deposit today into an account with quarterly compounding interest in an APR of 4.5% in order to have $25,000 in 8 years for down payment on a house? Assume no additional deposits are made. ### Financial Mathematics Problem: Compound Interest Calculation**Question:**How much must you deposit today into an account with quarterly compounding interest and an APR of 4.5% in order to have $25,000 in 8 years for a down payment on a house? Assume no additional deposits are made.#### Explanation:To solve this problem, we need to use the formula for the present value of a compound interest account:\[ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \]Where:- $ PV $ is the present value (the amount you need to deposit today),- $ FV $ is the future value (the amount you want to have, $25,000),- $ r $ is the annual interest rate (APR, 4.5% or 0.045),- $ n $ is the number of times the interest is compounded per year (quarterly compounding, so $ n = 4 $),- $ t $ is the number of years the money is invested (8 years).#### Calculation Steps:1. Identify given values: - $ FV = $25,000 $ - $ r = 4.5\% = 0.045 $ - $ n = 4 $ - $ t = 8 $ years2. Substitute the values into the formula:\[ PV = \frac{25,000}{(1 + \frac{0.045}{4})^{4 \cdot 8}} \]3. Simplify and solve the equation:\[ PV = \frac{25,000}{(1 + 0.01125)^{32}} \]\[ PV = \frac{25,000}{(1.01125)^{32}} \]\[ PV = \frac{25,000}{1.4226516} \]\[ PV \approx 17,579.55 \]#### Conclusion:In order to have $25,000 in 8 years for a down payment on a house, you must deposit approximately $17,579.55 into the account today, assuming quarterly compounding interest at an APR of 4.5% and no additional deposits.

Given as, 8 years is $25,000 and APR of 4.5%.

Answered: mpounding interest and an APR of 4.5%…

Math

Advanced Math

mpounding interest and an APR of 4.5% in sume no additional deposits are made.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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