Answer: $43,019.24
Explanation:
To determine how much needs to be deposited today in order to have $55,000 in 5 years, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($55,000 in this case)
P = the initial deposit
r = the annual interest rate (5% in this case)
n = the number of times interest is compounded per year (assuming annual compounding in this case)
t = the number of years (5 years in this case)
To find the value of P, we rearrange the formula:
P = A / (1 + r/n)^(nt)
Substituting the given values, we get:
P = 55000 / (1 + 0.05/1)^(1*5)
P = 55000 / (1 + 0.05)^(5)
P = 55000 / (1.05)^5
P ≈ 55000 / 1.27628
Calculating this expression, we find that P is approximately $43,019.24.
Therefore, approximately $43,019.24 needs to be deposited today into the account in order to have $55,000 in 5 years for the down payment on a house.
I hope this helps :)