QQuestionAccounting
QuestionAccounting
Amaki's company Itd. received a $200 bill for copying services dated April 27. The terms on the invoice were 3 / 10 EOM. The firm paid the bill on June 2. How much did it pay?
QUESTION 3
Abena receives $5,000 semi annually from his grandmother's estate. He invests the money at 3.8% compounded semiannually. How much will he have after two years investing as an annuity due?
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Answer
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Step 1:: First, we need to determine the total number of compounding periods.
Since Abena receives money semi-annually and the interest is compounded semi-annually, the number of compounding periods is equal to the number of payments. Number of compounding periods = Number of payments
Step 2:: Calculate the number of payments.
Abena receives $5,000 every six months, and there are two six-month periods in a year. So, over two years, there will be: Number of payments = 2 years * (2 six-month periods / year) = 4 six-month periods
Step 3:: Now, we can calculate the future value of the annuity using the compound interest formula:
FV = P \times \left(1 + \frac{r}{n}\right)^{nt}
where: - FV is the future value of the annuity - P is the payment amount ($5,000) - r is the annual interest rate (3.8%) expressed as a decimal (0.038) - n is the number of times interest is compounded per year (2, since it's compounded semi-annually) - t is the time the money is invested for (4 six-month periods or 2 years)
Step 4:: Plug the values into the formula:
FV = $5,000 \times \left(1 + \frac{0.038}{2}\right)^{2 \times 4}
Step 5:: Calculate the result:
FV = $5,000 \times \left(1 + \frac{0.038}{2}\right)^{8} \approx $5,000 \times 1.03948176 \approx $5,197.41
Final Answer
After two years, Abena will have approximately $5,197.41 in his account.
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