Kevin will make payments of 150 at the end of every month to...

Kevin will make payments of $150 at the end of every month to settle a loan of $1,000 at 4.50% compounded semi-annually that he received to purchase a television. a. How many deposits will he have to make? Round up to the next whole number b. How long will he have to make these payments? years months

Transcript

00:01 So tiffany wants to accumulate a sum of 55 ,000 by making regular deposits of 1 ,000 at the end of every month, so 12 times per year, in a fund that earns an interest rate of 6 .5%, so 0 .065 compounded monthly.

00:26 And then the question is, how many deposits does she need to make to reach this goal? so the number of deposits is the time period that we need to do this.

00:40 And the formula here is the sum of an annuity is equal to the deposits that are made regularly, times 1 plus the interest rate, r over n, to the...

00:57 Normally we do nt for the number of years in times the number of periods per year, but here i just want the number of months, so let's call that t then.

01:11 This is the number of months.

01:16 And you subtract 1 and divide by r over n.

01:20 So if you want to solve that for t, we can do that here, because we have everything else.

01:25 I have 55 ,000 is equal to 1 ,000 times...

01:31 Let's see here...

01:32 R over n is 0 .065 divided by 12, which is equal to...

01:54 1 .005416, with repeating sixes to the t, minus 1 divided by 0 .005416.

02:04 And i'm gonna divide both sides by a thousand.

02:09 It gets rid of all those zeros.

02:12 Then i'm gonna multiply by whatever i have in the denominator here.

02:18 So i get 55 times that is equal to 0 .297916 is equal to 1 .005416, with repeating sixes minus 1.

02:40 And then i'm gonna add 1 to this.