Question

Your parents have accumulated a $130,000 nest egg they have been planning to use this money to pay college cost to be incurred by you and your sister Courtney. However, Courtney has decided to forgo college and starting nail salon. Your parents are giving Courtney $34,000 to help her get started, and they have decided to take year and vacations costing $10,000 per year for the next four years. Use 6% as the appropriate interest rate throughout this problem.

A. How much money will your parents have at the end of four years to help you with graduate school which you will start then?

Funds available for graduate school:

B. You plan to work on a masters and perhaps a PhD. If graduate school cost $30,820 per year, approximately how long will you be able to stay in school based on these funds?

Numbers of years:

Answer 1

Funds available	130,000
Funds given to Courtney	(34,000)
Funds available	96,000
Future value after 4 years	96000*(1+6%)^4
Future value after 4 years	121,197.79
Future value of vacation amount spent	10000*((((1 + 6%) ^ 4) - 1) / 6%)
Future value of vacation amount spent	43,746.16
Funds available after vacation	121197.79-43746.16
Funds available after vacation	77,451.63
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
77541.63=	30820* (((1-(1 + 6%) ^- n)) / 6%)
77541.63/30820	=(((1-(1 + 6%) ^- n)) / 6%)
2.52	=(((1-(1 + 6%) ^- n)) / 6%)
2.516*6%	=1-(1 + 6%) ^- n
0.15	=1-(1 + 6%) ^- n
0.85	=(1 + 6%) ^- n
log 0.85	-n*log 1.06
-0.07058107=	-n*0.02530587
n=	=0.07058107/0.02530587
n=	2.79	Years