Question

You plan to start saving for your son's college education. He will begin collage when he turns 18 years old and will need $4,000 at that time and in each of the following three years. You will make a deposit at the end of this year in an account that pays 6% compounded annually as well as an identical deposit at the end of each year, with the last deposit occurring when he turns 18. If an annual deposit of $1,484 will allow you to reach your goal, how old is your son now? Please explain with formulas manually and if possible financial calculator hp10 bll I need to understand it base on the Graham Smart Megginson Corporate Finance book explanation chapter 3 The time Value of Money. Thank you in advance

Answer 1

The fees of college = 4000
Number of total payments = 4
Value of all fees at age 18 using annuity due formula = (1+r)*PMT*(1-(1+r)^-n )/r = (1+6%)*(4000)*(1-(1+6%)^-4 )/6% = 14,692.05

Number of periods of payment = N( deposited annually)
Rate = 6%
FV = 14,692.05
PMT = 1484
Using FV of annuity formula
FV = PMT*((1+r)ⁿ-1)/r
14,692.05 = 1484*((1+6%)ⁿ-1)/6%
14,692.05*6%/1484 = 1.06ⁿ-1
1.06ⁿ = 1+0.594018 = 1.594018
Applying log on both sides
n = Log1.594018/log1.06 = 8 years

So age of son now = 18-8 = 10 years

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