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