How do I solve the following word problem? How much money will she have altogether from the two accounts after 5 years?  Judy has $8,000 to invest.  She invests $6,000  in an account that pays an annual percentage rate of 5% compounded quarterly.  Then she decides to invest the remaining money in a speculative account that is advertised at 8% compounded monthly.   Assume she gets lucky and the speculative account pays at 8% the entire time.  Round your answer to the nearest dollar.

Expert Answers

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To find the amounts in each investment account, use the formula for compound interest:

`A=P(1+i)^n`  where A is the amount in the account after the investment period is complete, P is the amount invested initially, i is the interest rate per period and n is the number of investment periods.

For the first account, `P=6000` , `i=0.05/4=0.0125` since the investment is quarterly, which means that `n=5 times 4=20` .  This means that the first account has the amount:

`A=6000(1.0125)^20=7692.22`

The speculative account has `P=2000` , `i=0.08/12=0.0066667` since the account is monthly, which means that `n=5 times 12 = 60` .  The second account has:

`A=2000(1.00666667)^60=2979.69`   

The amount in the two accounts after 5 years is `7692.22+2979.69 approx 10672` .

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