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# Payments and Present Value

Payments of 5000 and 7000 are due 3 and 5 yrs respectively from today. They are to be replaced by two payments due 1 1/2 and 4 yrs from today. the first payment is to be half the amount of the 2nd payment. what should the payments if money can earn 7.5% compounded semiannually??

ans: 3711.68
7423.35

Manuela purchased a boat for 2000 down with the balance to be paid by 36 monthly payments of 224.58 including interest at 10% compounded monthly.

what was the purchase price of the boat?
what is the balance owed just after the 9th payment?

How much larger will the value of an rrsp be at the end of 25 yrs if the contributor makes month end contributions of 300 instead of year end contributions of 3600? in both cases the rrsp earns 8.5% compounded semi annually.

what will the amount be in an rrsp after 25 yr if contribution of 2000 are made at the beginning of the year for the first 10 yrs and contributions of 4000 are made at the beginning of each year for the subsequent 15 yrs? assume that the rrsp will earn 8% compounded quarterly.

what is the current economic value of an annuity due consisting of 22 quarterly payments of 700, if money is worth 6% compounded quarterly for the first 3 yrs, and 7% compounded thereafter?

#### Solution Preview

Answer 1: First we need to determine the PV of the 5,000 and 7,000 payments in Years 3 and 5 respectively.

PV of \$5,000 payment = 5000/(1.075^3) = 4024.802848
PV of \$7,000 payment = 7000/(1.075^5) = 4875.910426
Net PV = 8900.713274

Now we need to replace it with two payments. Use the following formula:
8900.713274 = (x/2)/(1.075^1.5) + x/(1.075^4)

where x is the payment amount in year 4.

Solving for x we get x=7433.375977
and x/2 = \$3,716.688

The slight difference in answer is due to rounding.

Use the ...

#### Solution Summary

The solution goes into a great amount of detail regarding the question being asked. Step by step explanation is provided for each part of the question which makes it very easy to follow along for anyone with just a basic understanding of the concepts. Overall, an excellent response to the question being asked.

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