word problem-$$

[Guest]

Leila is borrowing $65 000 for 4 years. She is deciding between a loan at 6.95% per annum, compounded montly, and a loan at 7% per annum, compounded annually.

a) Predict which loan is the better deal.
b) How much interest is paid on the loan that is the better deal?


I got the wrong ans. for this one, I'm thinking I used the wrong formula..coud you tell me which one you would use, and why.
Thanks

 

[TchrWill]

The formula for calculating a monthly loan payment is R = Pi/[1 - 1/(1+i)^n] where R = the periodic payment, P = the principal, or debt to be paid off, n = the number of payment periods over which the payments will take place, and i = the periodic interest rate in decimal form. The interest rate for a loan is usually quoted as an annual rate such as 8%. In the formula the first thing we do is convert this to i = .08 when considering annual payments.
If payments are to be made monthly, i = .08/12 = .006666 as the monthly interest rate. An example will illustrate the use of the formula.

Lets say you want to borrow $10,000 for a home improvement, to be paid off monthly over a period of 5 years, with an annual interest rate of 8%. So P = 10,000, n = 5 x 12 = 60, i = .08/12 = .006666. Then we have R = 10000(.006666)/[1 - 1/(1+.006666)^60] = 66.66/[1 - 1/(1.489790] = 66.66/.328764 = $202.76 per month. As simple as that. Over the life of the loan you will pay $12,165.49 back to the bank thereby incurring the cost of $2,165.49 for the priviledge of borrowing the money.

This should enable you to determine your answers.

 

[tkhunny]

4 years. She is deciding between a loan at 6.95% per annum, compounded montly

(1+(0.0695/12))⁴⁸ = 1.31942766

a loan at 7% per annum, compounded annually.

(1.07)⁴ = 1.31079601

Well, if you pay back nothing until the end, that's pretty clear.

Is there a payment plan?

 

[Guest]

R = Pi/[1 - 1/(1+i)^n so you use this formula then? I thought you would use A=P(1+i)^n..and I thought that the 6.95 plan would be better but it's not

 

[Denis]

That's (1.07)^4, TK...bad boy...

If it's a monthly payment loan, then the compounding monthly
rate becomes 12[(1.07)^(1/12)-1] = .0678497~;
that's 6.78~ compared to 6.95 : again, easy to see which is cheaper.

Monthly payments will be 1550.03~ and 1555.00~ respectively;
so figure out how much is saved from the difference of those payments; OK?

 

[tkhunny]

Corrected above...

I repeat, "Is there a payment plan?" We're just guessing, here.