A 4-year annuity of eight $11,400 semiannual payments will begin 9 years from no
ID: 2383000 • Letter: A
Question
A 4-year annuity of eight $11,400 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.
If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
$
The answer is NOT 36460.15
If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Explanation / Answer
Step 1: Calculate the Semi-Annual Effective Rate of Interest:
The semi-annual effective rate of interest can be calculated with the use of following formula:
Effective Rate of Interest = (1+Interest Rate)^n -1 where Interest Rate would be taken as monthly interest rate (since it is given as APR)
Monthly Interest Rate = 11%/12
Effective Rate of Interest (Semi-Annual) = (1+11%/12)^6 - 1 = 5.63%
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Step 2: Calculate the Present Value at 9 Years from Now:
The formula for calculating present value is:
Present Value = Payment*[(1-(1+r)^-n)/r]
Using the information provided in the question and effective rate of interest calculate above, we get,
Present Value 9 Years from Now = 11,400*[(1 -(1+5.63%)^-8)/5.63%] = $71,816.23
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Step 3: Calculate the Present Value Now:
Current Value of Annuity = Present Value 9 Years from Now/(1+r)^n = 71,816.23/(1+5.63%)^(9*2) = $26,794.86 (answer)
(Please note, there can be a slight difference in the answer on account of rounding off)