An investment in a lease offers returns of 1900 per month...

An investment in a lease offers returns of $1900 per month due at the beginning of each for 5 years. What investment is justified if the returns are deferred for 1 years and the interest required is 8% compounded quarterly ? Question content area bottom Part 1 An investment of $ enter your response here is justified.

Transcript

00:01 Hey folks, so we've got a question here about compounded interest.

00:05 So if we invest $5 ,000 10 years ago, and then we're going to deposit another $5 ,000 after four and eight years, we're wondering how much we would have.

00:14 If our interest rate was 9 .2 % compounded quarterly for the first two years, 8 .75 % compounded monthly for six years after that, and then 9 .8 % compounded semi -annually for the last two years.

00:29 So let's recall quickly that the amount of money you have after time t, this is your principal amount times 1 plus the rate divided by the number of times compounded yearly raised to the n times t power.

00:47 Okay, so we need to compute a few different things.

00:50 So first, we have 9 .2 % compounded quarterly for the first two years, right? and i have 5 ,000 in the account during that time.

01:00 So after two years, the amount i will have is my initial investment, the principal, times one plus the rate, which was 9 .2%, which i write as 0 .092 as a decimal, right? and then compounded quarterly.

01:24 So i put a 4 down here.

01:27 And then times 4, or then the nt, part, so n is 4, and t is two years, so i'm doing the first two years, so it's to the eighth power here.

01:40 And let's call this p sub two.

01:44 I'm going to call this number p sub two.

01:45 So at this point, you could put this in your calculator and get a number, just pretend this number is p sub two, and then we'll go on with the computation.

01:53 So what's next? we, our rate changes to 8 .75 % now, compounded monthly, but we don't put in more money until year four.

02:05 So next, we need to compute what is p4? how much am i going to have after four years? well, that's my principal starting, so we're starting from two years in.

02:17 And so my principal now, i'm just taking p2 as my principal.

02:23 And then, so that's some number.

02:24 That's the amount i have after two years.

02:26 And then i'm going to see how much i get when i do two more years at this new rate.

02:30 So it's one plus 0 .0875.

02:36 That's my new rate of 8 .75 % divided by.

02:41 So now we're compounding monthly, so i need a 12 here.

02:44 And this is for another two years, because then i need to refine my formula again because i'm depositing another $5 ,000.

02:51 So this becomes, so up here it's 12 times two, which is 24.

02:59 Okay.

03:00 Finally, two years, so at this point, we've found how much money i have after four years.

03:06 It's this amount here.