Question

A fire department plans to buy a truck in 3 years to, this trick would cost $ 625,000, but the cost is increasing at the rate of 4% annually. Find the semiannual payment needed to accumulate funds to buy the truck if money earns 16% compounded semiannually.

Answer 1

Answer - For Solving this question, we will first calculate the cost of truck after 3 years, since the company would be able to buy it only after 3 years.

So Cost ofTruck( at the end of 3 years) = $625,000(1.04)^3

So Cost of Truck after 3 years = $703,040

We have to compute semi annual payments which when paid semi annually, will give us exact $703,040 as at end of 3 years.
Here we will use the PMT function of excel to determine the installment amount-

A pmt function asks for above categories. In our case
rate = 8% compunded semianually, (Here annual interest rate = 16%, so for half year = 16%/2 = 8%)
period = 6 ( as 3 years will have 2 semi annual payments each so 3*2)
pv will be blank
FV = Future value we want, So i our case we want $703,040 as our future value so we will input this amount.
It will look like this and solving it we will get-
Semi Annual Payment Amount = $95,835.17

So semi annual payments of $95,835.17 will be required by the company to arrange the desired amount to purchase the truck.

Kindly comment in case of any concerns/doubts. Happy to Help.
Thank You, Stay Safe.