Time Value of Money calculations are a great way to figure out how much payments will be on loans or how much we need to save over time to

achieve our financial goals. The calculation always uses the variables: N $($number of periods$),$ I$/$Y $($Interest rate per period$),$ PMT $($Payment Amount

per period$),$ PV $($Present Value$),$ and FV $($Future Value$).$ Given $4$ variables we can calculate the $5$th variable. If you want to buy a new car, you can

figure out the payments $($PMT$)$ if you know the amount of the loan $($PV$),$ the interest rate $($I$/$Y$),$ and the number of payments you want to make $($N$).$

What about future value? Well, with a loan we want to pay that thing off, so the FV is $$0.$

For example: I am looking at a Tesla Model S Dual Motor. It has a $$75,990$ sticker$($internet$)$ price that goes up to a $$83,064$ OTD price $($out$-$the$-$

door$)$ including taxes, fees, and delivery$/$destination fee. I want to put $$10,000$ down, my estimated interest rate is $4\mathrm{.}9\%$ and I want a loan for $6$

years $(72$ months$).$ Now I can figure out my payment using my financial calculator.

N $=6$ years x $12$ months $=72$ pay periods

I$/$Y $=4\mathrm{.}9\%/12=0\mathrm{.}408333\%$ per month $($use at least $6$ decimals$)$

PV $=$ $$83,064-$ $$10,000$ down payment $=$ $$73,064$ financed

FV $=$ $$0($pay the loan off$)$

CPT PMT $($Solve for PMT$)=??-$$$1,173\mathrm{.}30($it is negative because I$\text{'}$m paying it every month, that money leaves my bank account$)$

So$,$ my payments will be $$1,173\mathrm{.}30$ per month for $6$ years if I want to buy that Tesla.

I can take this calculation a step further by figuring out the total cost of the car and the total interest I'll pay on the loan.

Take the payment and multiple it by the number of payments to get the total payments.

Add the down payment to get the total cost of the car.

Then, Subtract the initial OTD price of the car to get the amount of interest paid over the loan.

$$1,173\mathrm{.}30$x $72=$ $$84,477\mathrm{.}60$ in total payments

$$84\mathrm{.}477\mathrm{.}60+10\mathrm{.}000=$ $$94\mathrm{.}477\mathrm{.}60$ is the total cost of the car Yep $$94\mathrm{.}5$k for a car with a $$76$k sticker price$).$

$$94\mathrm{.}477\mathrm{.}60-83\mathrm{.}064=$ $$11\mathrm{.}413\mathrm{.}60$ in total interest paid over the course of the loan.

Discussion Question

Find a car, maybe your dream car, and look it up on a dealership's website. Find the price $($Try to find the out$-$the$-$door price. If you can't, add

another $7\%$ to estimate taxes and fees. hint multiply the price listed by $1\mathrm{.}07$ to add $7\%$ to the list price$),$ estimate a down payment you will use,

and then calculate your estimated payment for $72$ months. Use $7\mathrm{.}9\%$ for your I$/$Y $($don$\text{'}$t forget to convert it to monthly by dividing by $12).$ Then

figure out the total payments, total cost of the car, and the total interest you'll pay over the course of the loan. Use my example as a guide. Post

your results and comment on other posts.