You are chairperson of the investment fund for the Continental Soccer League. Yo

Question

You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semiannual payments to be compounded semiannually to accumulate a sum of $310,000 after ten years at a 14 percent annual rate (20 payments). The first payment into the fund is to take place six months from today, and the last payment is to take place at the end of the tenth year. Use Appendix A and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. Determine how much the semiannual payment should be. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Semi-annual payment $ On the day after the sixth payment is made (the beginning of the fourth year), the interest rate goes up to an annual rate of 16 percent. This new rate applies to the funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semiannually on all funds. b. Determine how much the revised semiannual payments should be after this rate change (there are 14 payments and compounding dates). The next payment will be in the middle of the fourth year. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Revised semi-annual payment $

Explanation / Answer

Part A)

The semi-annual payment can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value (if any) and FV = Future Value.

________

Here, Rate = 14%/2 = 7%, Nper = 10*2 = 20, PV = 0 and FV = $310,000 [we use 2 since the payments are semi-annual]

Using these values in the above function/formula for PMT, we get,

Semi-Annual Payment = PMT(7%,20,0,310000) = $7,561.81

________

Part 2)

Step 1: Calculate the Future Value of Old Payments (from Part 1) After 6 Period

The future value of old payments after 6 periods can be calculated with the use of FV (Future Value) function/formula of EXCEL/Financial Calculator. The function/formula for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Semi-Annual Payment and PV = Present Value (if any).

_________

Here, Rate = 14%/2 = 7%, Nper = 6, PMT = $7,561.81 and PV = 0

Using these values in the above function/formula for FV, we get,

Future Value of Old Payments after 6 periods = FV(7%,6,7561.81,0) = $54,091.83

_________

Step 2: Calculate the Future Value of the Old Payments after 14 Periods at Revised Rate

The future value of a lumpsum payment can be calculated with the use of following formula:

Future Value after 14 Periods = Amount*(1+Rate)^(Periods) = 54,091.83*(1+16%/2)^(14) = $158,878.18

_________

Step 3: Calculate the Amount to be Accumulated after Adjustment for Old Payments

The amount to be accumulated after 14 periods at revised rate after adjustment for old payments can be calculated as follows:

Amount to be Accumulated after Adjustment for Old Payments = 310,000 - 158,878.18 = $151,121.82

_________

Step 4: Calculate the Value of Revised Semi-Annual Payment

The semi-annual payment can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value (if any) and FV = Future Value.

________

Here, Rate = 16%/2 = 8%, Nper = 14, PV = 0 and FV = $151,121.82 [we use 2 since the payments are semi-annual]

Using these values in the above function/formula for PMT, we get,

Semi-Annual Payment = PMT(8%,14,0,151121.82) = $6,240.86

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