Question

Kreskin borrowed $10000 at an annual interest rate of 3% and paid off the loan (principal and interest), after several years with a $15580 check. How many years did it take Kreskin to repay the loan?

Answer 1

@R.Hamza17

Answer 2

Hello, R_S! I'm assuming that this is a case of interest compounded annually.

If that's the case, the appropriate formula is \[A=P(1+\frac{ r }{n })^{nt}\]

Answer 3

hmmmm is that for compound interest?

Answer 4

I thought we need to use F = P(1+i)^n

Answer 5

were r is the annual interest rate, expressed as a decimal fraction, P is the original principal, A is the final amount, and n is the number of years over which interest accrues.

I'm assuming that it is compound interest. We could do the problem either way: simple interest or compound interest. Your choice.

Answer 6

Okay n and A make sense. What does principal mean?

Answer 7

Your F = P(1+i)^n is fine if interest is paid annually (once per year), EXCEPT that I'd prefer you use " t " for time, not "n" .

Answer 8

P=principal=original loan amount. How much was that?

Answer 9

I'd like to use t as well but I think the university I am attending would rather me use n or at least my instructor would like me to use n. P = 15580

Answer 10

I do object a bit to that, r_s, because n is commonly used to denote how many times interest is paid EACH :YEAR and t to denote how many years.

Answer 11

ohhh I see. Okay I get what you are saying..

Answer 12

Let n=1 in the following equation and see what you get.\[A=P(1+\frac{ r }{n })^{nt}\]

Answer 13

hold on

Answer 14

t = 15

Answer 15

Nice work!
15 what?

Answer 16

15 years.

Answer 17

Okay thanks for your help. Why did you use F = P(1+(i/n))^n*t

Answer 18

sure thing. Sound reasonable?

Answer 19

I actually prefer that equation over the other one cuz it makes more sense to me

Answer 20

Because that's a more general formula. Suppose that your bank pays you interest on your savings quarterly. Then n would be 4.

Twice a year? Then n would be 2.

If interest is compounded continuously (which does happen), then\[F=Ae ^{rt}\]

Answer 21

So Kreskin paid a total interest of $5580

Answer 22

Bet you didn't know you wanted to know all that. ;)

Answer 23

Yes, that's right. He must have money burning holes in his pockets.

Answer 24

No makes a little more sense, especially seeing the exponential function.

Answer 25

So, could you give me $1,000,000 to earn interest compounded continuously at 4%? ;)

Answer 26

Yes, but I don't want to because I have more hw I need to do. If I have anymore additional questions I will post them up.

Answer 27

In 5 years that'd be $1,221,402.76.

Answer 28

;)