You would like to have $750,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 4.2% compounded quarterly?
future value = (payment)[((1+i)^n-1)/i]
750000 = P[(1.042^(4*25)-1)/0.042]
750000 = P[1433.4]
payment = $523.23
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a) How much should you deposit each quarter?:: 523.2307
b) How much total money will you put into the account?:: $52,323.07
c) How much total interest will you earn?:: 750,000-52323 = 697,676.93
To check your answer,
523.23*4*25=52323 which is only about 6% of the final amount, which seems too low.
So looking at your working:
Future value = (payment)[((1+i)^n-1)/i]
is basically correct, if we assume
i=interest per period.
rate 4.2% is annual interest (by normal convention), so the interest per period is
i=4.2%/4=1.05%=0.0105
If you repeat the same calculations with the corrected value of i, then you should find the quarterly payment to be over four thousand dollars.
Parts (b) and (c) would be correct if you had the correct answer for (a)
Post your answers again if you wish to confirm.
To determine how much you should deposit each quarter, you can use the formula for future value of a series of payments:
Future Value = Payment * [((1 + interest rate/number of periods)^number of periods - 1) / (interest rate/number of periods)]
In this case, you want to have $750,000 when you retire in 25 years, and the interest rate is 4.2% compounded quarterly.
Thus, the equation becomes:
750,000 = P * [((1.042^(4*25)-1)/0.042)]
Simplifying this equation, we calculate:
750,000 = P * 1433.4
To solve for P, divide both sides of the equation by 1433.4:
P = 750,000 / 1433.4
P ≈ $523.23
Therefore, you should deposit approximately $523.23 each quarter to accumulate $750,000 in 25 years.
Now let's address the additional questions:
a) How much should you deposit each quarter?
Answer: $523.23
b) How much total money will you put into the account?
To calculate the total money you will put into the account, multiply the quarterly deposit by the number of quarters:
Total Money = Payment * Number of Quarters
Total Money = $523.23 * 100 (assuming 25 years * 4 quarters per year = 100 quarters)
Total Money ≈ $52,323.07
Therefore, you will put approximately $52,323.07 into the account over the course of 25 years.
c) How much total interest will you earn?
To calculate the total interest earned, subtract the amount you put into the account from the desired future value:
Total Interest = Future Value - Total Money
Total Interest = $750,000 - $52,323.07
Total Interest ≈ $697,676.93
Therefore, you will earn approximately $697,676.93 in interest over the course of 25 years.