Solve the problem.
-Suppose you start saving today for a $20,000 down payment that you plan to make on a house in 10 years. Assume that you make no deposits into the account after your initial deposit. The account
Has quarterly compounding and an APR of 3%. How much would you need to deposit now to
Reach your $20,000 goal in 10 years?

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of a single lump sum with compound interest: $FV = PV(1 + \frac{r}{n})^{nt}$, where $FV$ is the future value, $PV$ is the present value (initial deposit), $r$ is the annual interest rate (in decimal form), $n$ is the number of compounding periods per year, and $t$ is the time in years. We're solving for $PV$, so we rearrange the formula to $PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$.Given: $FV = \$20,000$, $r = 0.03$ (3% annual interest rate), $n = 4$ (quarterly compounding), and $t = 10$ years.Plugging these values into the formula gives us:$$PV = \frac{\$20,000}{(1 + \frac{0.03}{4})^{4 \times 10}}$$$$PV = \frac{\$20,000}{(1 + 0.0075)^{40}}$$$$PV = \frac{\$20,000}{(1.0075)^{40}}$$$$PV = \frac{\$20,000}{1.349858807576003}$$$$PV = \$14,832.96$$Therefore, you would need to deposit \$14,832.96 now to reach your $20,000 goal in 10 years with the given conditions.

Solve the Problem. -Suppose You Start Saving Today for a $20,000 Down Payment