Question

Joann wants to save for her daughter's education. Tuition costs $9,000 per year in today's dollars. Her daughter was born today and will go to school starting at age 18. She will go to school for 4 years. She can earn 12% on her investments and tuition inflation is 6%. How much must she save at the end of each year if she wants to make her last savings payment at the beginning of her daughter's first year of college?

A. 1,889

B. 2,117
      
C. 2,370
      
D. 1,700

Answer 1

Tuition costs of daughter at age 18(Year 1 of college) = 9000 * ( 1+inflation )¹⁸ =9000* (1+6%)¹⁸ = 25689.05
Tuition costs of daughter at (Year 2 of college) = 9000 * ( 1+inflation )¹⁹ =9000* (1+6%)¹⁹ = 27230.39
Tuition costs of daughter at (Year 3 of college) = 9000 * ( 1+inflation )²⁰ =9000* (1+6%)²⁰ = 28864.22
Tuition costs of daughter at (Year 4 of college) = 9000 * ( 1+inflation )²¹ =9000* (1+6%)²¹ = 30.596.07

Value of tuition fees at age 18 = 25689.05 + 27230.39/(1+ 12%) +  28864.22/(1. +12%)² + 30.596.07
/(1+12%)³ = 94789.96

Rate = 12%
Number of Period n = 18
FV = PMT *( ( 1+r)ⁿ - 1)/r
94789.96 = PMT * ( ( 1+12%)¹⁸ -1)/12%
PMT = 1700.28

SO option d 1700 is the correct option

?Best of luck. God Bless