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.