You would like to have $550,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 5.5% compound quarterly?
a) How much should you deposit each quarter?
b) How much total money will you put into the account?
c) How much total interest will you earn?
To find the answers to these questions, we can use the formula for the future value of an investment with compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (amount to be deposited each quarter)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Now let's solve each part of the problem step by step:
a) To find how much you should deposit each quarter, we need to rearrange the formula to solve for P:
P = FV / ((1 + r/n)^(nt))
Plugging in the given values:
FV = $550,000
r = 5.5% = 0.055 (in decimal form)
n = 4 (since interest is compounded quarterly)
t = 25
P = $550,000 / ((1 + 0.055/4)^(4*25))
Calculating this expression will give you the amount you need to deposit each quarter.
b) To find the total money you will put into the account, you need to multiply the quarterly deposit amount by the number of quarters in 25 years. Since there are 4 quarters in a year, you can multiply the quarterly deposit by the number of years:
Total money = P * (4 * t)
Now, substitute the value of P and t into this equation to find the total money you will put into the account.
c) To find the total interest earned, subtract the principal amount (total money deposited) from the future value:
Total interest = FV - Principal amount
Now, substitute the values of FV and the total money deposited into this equation to find the total interest earned.
By following these steps, you will be able to find the answers to all the given questions.