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Homework answers / question archive / Suppose you will receive $14,000 in 9 months and another $14,000 in 22 months
Suppose you will receive $14,000 in 9 months and another $14,000 in 22 months. If the discount rate is 7% per annum (compounding monthly) for the first 12 months, and 12% per annum (compounding monthly) for the next 10 months, what single amount received today would be equal to the two proposed payments? (answer to the nearest whole dollar; don't include the $ sign or commas) Answer:
You are given the equation below. FV = (1 + i)10 – 1)(1+i) () Which of the following statements is CORRECT? Select one: A. The equation will indicate the future value of an annuity of 10 payments, immediately after the 10th payment B. The equation will indicate the future value of an annuity due of 10 payments at the end of the 10th period. C. The equation will work where I make 10 annual payments commencing at the end of the first year if I wish to know the value at the beginning of the 10th year. D. None of the above are correct.
Solution.>
In this particular question, basically we have to find the sum of present value of both the amounts. The PV of both the amounts will be equal to the single amount we receive today.
For the $14,000, time period = 9 months and rate = 7%
Present Value = Amount / ( 1+rate/12)^months
Present Value = $14000 / ( 1+7%/12)^9
Present Value = $13,285.99
For the $14,000, time period = 22 months and rate = 7% for first 12 months and 12% for next 10 months
Present Value at the end of 12 months = $14000 / ( 1+12%/12)^10
Present Value at the end of 12 months = $12,674.02
Present Value now = Present Value at the end of 12 months / ( 1+7%/12)^12
Present Value now = $12,674.02 / ( 1+7%/12)^12
Present Value now = $11,819.58
Total Amount = $13,285.99 + $11,819.58
Total Amount = $25,106
answer is b
Annuity due. The second type of annuity is known as an annuity due. This is the type of payment we are focusing today and an annuity due requires the payment to be made at the beginning of the payment period. The payment typically covers the balance owed for the remaining period following the payment.
The future value of an annuity due formula is used to predict the end result of a series of payments made over time, including the income that is made from their associated interest rates. The term “value” refers to the potential cash flow that a series of payments can achieve. So by looking at the future value, we are calculating this potential at a future date in time.
It is possible to calculate the future value of an annuity due by hand. To do this, you could make a chart to list the amounts of the payments being made. You would identify the payment periods and the set interest rate through the time limit you have set. However, this would take a lot of extra work and time. Thankfully, the formula can help you promptly find the answer.
Future Value of an Annuity Due Formula
FV = FV=C/r×[r(1+r)^n−1?]×(1+r)
