Question

Suppose you are planning to spend $1766 annually for vacation during the next 30 years. You...

Suppose you are planning to spend $1766 annually for vacation during the next 30 years. You are offered to pay $30,000 now so that annual expenses of your vacations for the next 30 years will be taken care of. The annual interest rate is 6%. Calculate the amount that is saved if you pay $1766 annually instead of $30,000 now (Hint: calculate 30,000 - PV($1766 paid annually)).

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Answer #1

In order to calculate the saving, we need to calculate the present value of annual payment of $1766 annually for 30 years, at 6%. The present value of this annuity compared to the $30,000 paid today, we will get the saving if we pay $1766 annually instead of $30,000 now.

PV of an annuity is mathematically represented as:

Substituting r = 6%, n = 30, P = $1766, we get equation as:

PV = $24,308.69

Now, this is the PV of annual payments to be made for 30 years.

Savings = $30,000 - $24,308.69 = $5,691.31

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