Today is your birthday, and you decide to start saving for your college education. You will begin college on your 18th birthday and will need $4,000 per year at the end of each of the following 4 years. You will make a deposit 1 year from today in an account paying 12% annually and continue to make an identical deposit each year up to and including the year you begin college.
If a deposit amount of $2,542.05 will allow you to reach your goal, what birthday are you celebrating today?

10 years, 175 days

Explanation:

Given the following ;

Payment per period(PMT) = $4000

PERIOD(n) = 4 years

Interest(r) = 12% = 0.12 per annum

Firstly,

Calculating the present value(PV) of the payment per period at 12% rate for 4 years

PV = [PMT(1 - (1 + r) ^-n)] ÷ r

PV = [4000 (1 - (1 + 0.12)^-4)] ÷ 0.12

PV = [4000 ( 1 - (1.12)^-4)] ÷ 0.12

PV = [4000 ( 1 - 0.635518078)] ÷ 0.12

PV = $12,149 (to the nearest whole number)

Now we calculate the period ;

if a deposit of $2542 is made

PV = [P(1 - (1 + r) ^-n)] ÷ r

12149 = [2542(1 - (1.12)^-n)]÷ 0.12

1457.88 = 2542.05(1 - (1.12)^-n)

2542 - 2542(-1.12^-n) = 12149 ×1.12

Log0.42648 = - n * log1.12

n = 7.52 years

There for payment will be made for 7.52 years

Present age = 18 - 7.52 = 10.48

10.48years.

10years, 175 days

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