# Math Help - Interest

1. ## Interest

Here's the question.

Sarah Ling is seventeen (17) years old and has big plans to retire when she is fifty (50) years old. She estimates she will need $3,000 at the end of each month for thirty (30) years to live comfortably in her old age and guesses that the interest rate will remain constant at 5% compounded annually during that time. Sarah has$10,000 in savings today and plans to save $2,000 each year to achieve her goal. 1. What interest rate must Sarah obtain in order to meet her goal? 2. If Sarah can save$3,000 per year, what interest rate must she obtain at minimum to meet her goal? 3. If Sarah defers her retirement plans for five (5) years, and then starts adding $5,000 to her savings each year, will she meet her goal of retiring at five (50)? Assume the interest rate is 6.5% compounded annually for period of time until she reaches fifty (50) years of age. Using my financial calculator.... #1 -3,000 pmt 360 n 0.4074 comp pv = 565,988.4258 PV=PMT[(1-(1+I)^-n)/I] PV=3000[(1-1.004074)^-360)/0.004074] PV=565,988.4258 -10,000 pv -2,000 pmt 565,988.4258 fv n 33 comp i = 9.2619 % #2 8.0106 % It was not taught to use a formula for this But couldn't you use the above formula and isolate for "I"? #3 no -5000 pmt -10,000 pv 28 n 6.5 i comp fv = 429, 979.04 I used theses 2 formula to find the above answer fV=PMT[((1+I)^n)-1/I] fv=pv(1+I)^n Thank you very much to those that will participate. 2. you seem smart can you answer my question plz? i have a final exam tomorrow 3. Originally Posted by Meera123 you seem smart can you answer my question plz? i have a final exam tomorrow LOL...I am far from it. Just trying to learn. But what is your question? 4. Ryan took out a 30 year mortgage for$160,000 at 9.8% interest compounded monthly. After he made 12 years of payments he decided to refinance the remaining loan for 25 years at 7.2% interest compounded monthly. What willl be the balance on their loan 5 years after the refinance?

I would reeeally appreciate your help. I'm an 18 year old first year student in a university in Dubai and I'm reeeally dumb.

5. Pete, you have pressed all the RIGHT keys, including the rate conversion to .4074 in part#1:
youze a QUICK learner. We all stand up here and give you a standing ovation!!

An important question now is:
if you had no "financial calculator", could you get those same results using appropriate formulas?

6. Originally Posted by Wilmer
Pete, you have pressed all the RIGHT keys, including the rate conversion to .4074 in part#1:
youze a QUICK learner. We all stand up here and give you a standing ovation!!

An important question now is:
if you had no "financial calculator", could you get those same results using appropriate formulas?
Wilmer...thank you ver much for your comment. The reason I use my calculator is that my intructor prefers that i do it this way, dont know why. To prove to you that I have learned alot i will show you the other way...the algebraic equation way later when i have some more time.

7. Wilmer..I have edited my original post in red to show the calculation using the formula.

8. Originally Posted by petedam
PV=PMT[(1-(1+I)^-n)/I]
PV=3000[(1-1.004074)^-360)/0.004074]
PV=565,988.4258

-10,000 pv
-2,000 pmt
565,988.4258 fv
n 33
comp i = 9.2619 %

#2
8.0106 %

It was not taught to use a formula for this But couldn't you use the above formula and isolate for "I"?
No, the "I" cannot be isolated: trial and error is required (known as "iteration".
I wouldn't worry about it for now if I were you.

9. Originally Posted by Wilmer
No, the "I" cannot be isolated: trial and error is required (known as "iteration".
I wouldn't worry about it for now if I were you.
I think that will be comming up soon. I have never heard of "iteration" yet. Looking forward to it though.

Thanks,