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You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semi-annual payments to be compounded semi-annually to accumulate a sum of $250,000 after nine years at a 10 percent annual rate (18 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 ninth year.

a. Determine how much the semi-annual payment should be. (Round to whole numbers.)

On the day after the sixth payment is made (the beginning of the fourth year), the interest rate goes up to a 12 percent annual rate, and you can earn a 12 percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semi-annually on all funds.

b.Determine how much the revised semi-annual payments should be after this rate change (there are 12 payments and compounding dates). The next payment will be in the middle of the fourth year. (Round all values to whole numbers.)

Short Answer

Expert verified
  1. Semi-annual payment: $8,887.
  2. Revised semi-annual payment: $7,609.

Step by step solution

01

Definition of Annuity

A financial product or financial investment that provides the investor with a stream of fixed payments is known as an annuity. The investor starts receiving payment as the annuitization period gets over.

02

Calculation of semi-annual payment

Fund value after 9 years = $250,000

Semi-annualrate=102=5%

No. of payments = 18

Annualpayment=Futurevalue[1+rn-1r]=$250,000(1+0.05)18-10.05=$250,00028.13=$8,887

03

Calculation of revised semi-annual payment

FV=PMT×[1+in-1]i=8,886.56×(1+0.05)6-10.05=$60,445.58

FV=PV×(1+i)n =60,445.58×(1+6%)12=$121,628.38Requiredfundvalue=foudvalue-Estimatedaccumualtion=$250,000-$121,628.38=$128,371.62

RevisedAnnualpayment=Futurevalue[1+rn-1r]=$128,371.62(1+0.06)12-10.06=$7,609.49

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