A 5-year annuity of ten $6,200 semiannual payments will begin 9 years from now,

Question

A 5-year annuity of ten $6,200 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

If the discount rate is 9 percent compounded monthly, what is the current value of this annuity?

(Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Please show how you got your answer...DO NOT USE EXCEL.. I need to be able to do this problem by hand.

A 5-year annuity of ten $6,200 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

Explanation / Answer

Semiannual interest = (1+9%/12)^6 - 1 = 4.5852%

PV of annuity as of 9 years from now = 6,200 * (1-1/(1+4.5852%)^10) / (4.5852%) = 48,854

So PV of annuity as of now = 48,854 / (1+4.5852%) ^ (9*2) = 21,798.85

Answer: 21,798.85

Hope this helped ! Let me know in case of any queries.

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