To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we want to find the initial deposit (P), so we rearrange the formula as:
P = A / (1 + r/n)^(nt)
Given:
A = $20,000
r = 3% or 0.03 (as a decimal)
n = 4 (quarterly compounding)
t = 10 years
Plugging in the values, we get:
P = 20000 / (1 + 0.03/4)^(4*10)
Simplifying further:
P = 20000 / (1 + 0.0075)^(40)
P = 20000 / (1.0075)^40
Using a calculator:
P ≈ 20000 / 1.357595
P ≈ $14,738.01
Therefore, you would need to deposit approximately $14,738.01 now to reach your $20,000 goal in 10 years.
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?
1 answer
1 answer