At the end of each quarter, a 50-year-old woman puts $3000 in a retirement account that pays 5% interest compounded quarterly. When she reaches 60, she withdraws the entire amount and places it in a mutual fund that pays 6.9% interest compounded monthly. From then on she deposits $300 in the mutual fund at the end of each month. How much is in the account when she reaches age 65?

SCREW MATH

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To find out how much is in the account when the woman reaches age 65, we need to calculate the future value of the account at that time.

First, let's calculate the future value of the retirement account when she reaches age 60. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the account
P = the initial principal amount (the amount she put in at the end of each quarter)
r = the annual interest rate (5% in this case)
n = the number of times interest is compounded per year (quarterly in this case)
t = the number of years

Since she is depositing at the end of each quarter, we need to calculate the future value for 10 years (from age 50 to age 60).

t = 10 years

The formula becomes:

A = 3000(1 + 0.05/4)^(4*10)

Next, let's calculate the future value of the mutual fund when she reaches age 65. We can again use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the account
P = the initial principal amount (the amount she withdrew from the retirement account and placed in the mutual fund)
r = the annual interest rate (6.9% in this case)
n = the number of times interest is compounded per year (monthly in this case)
t = the number of years

Since she is depositing at the end of each month, we need to calculate the future value for 5 years (from age 60 to age 65).

t = 5 years

The formula becomes:

A = (3000*40)(1 + 0.069/12)^(12*5) + (300*12)((1 + 0.069/12)^(12*5) - 1)/(0.069/12)

Finally, to find out the total amount in the account when she reaches age 65, we need to sum up the future values of both the retirement account and the mutual fund.

Total Amount = Future Value of Retirement Account + Future Value of Mutual Fund

Total Amount = A (from the retirement account) + A (from the mutual fund)

Now, plug in the values for A (from the retirement account) and A (from the mutual fund) and calculate the total amount in the account when she reaches age 65.