00:01
In the given question, we are told that a couple purchasing a car can spend up to $400 per month for their loan payment.
00:14
Now, if they have $2 ,500 available for a down payment and are considering a five -year loan, how much can they spend on the car at each of the following rates? and two rates are given to us which are both compounded monthly.
00:31
So what we could first do is to list out the things that we have been told in the question.
00:37
So the payment that she can make, they can make.
00:43
The monthly payment, monthly payment they can do is $400.
00:52
The down payment, money, available for.
00:58
For down payment available for down payment for down payment is $2 ,500 and we are told that they are considering a five -year loan plan and the first interest rate that is given to us is 6 .2 percentage and it is compounded monthly.
01:28
It is compounded monthly, right? so what we could do over here first is we can list the, we can use the formula, use a formula to find the future value of this payment that she is making periodically.
01:48
So the future value of this payment can be found by taking the periodic payment that she is making times one plus the interest rate.
01:58
Raised to the power of n where n is the number of compounding periods divided by i so this is the formula that we are going to use over here right so the periodic payment that she is making is four hundred dollars and the interest rate that is that is being given over here 6 .2 percentage is the yearly rate so we should be dividing 6 .2 percentage with 12 so when we do this that is when we take 6 .2 percentage and divide it with 12 what we get over here as the value of i is 0 .00517 and this is what is raised to the power of n where we already told that n is the number of compounding periods right so the number of months the number of compounding periods would be number of compounding periods is compounding periods is equal to five years but since we are compounding it monthly we would have to take it in the form of in the in terms of month so five years in terms of months would be five times 12 which is 60 months so five years is 60 months so over here n would be equal to 60 this minus 1 divided by 0 .005167 and now on evaluating this what we get as the future value is 28 ,050, 28 ,050 .119 so in the question we are not specifically told to round the answer to any specific value so let's just take the future value as $28 ,050 right so now what we can do is once we have calculated the future value we can write the total they can spend on the car right total that can be spent on the car that can be spend on the car spend on the car spend on car spend on car is the 2 ,500 down payment plus the future value of the payments the monthly payments she is making so when we take 28 ,050 plus 2 ,500 we get a value of 30 ,550 $30 ,550...