How much should a mother invest at the time her son is born to provide him with $55,000 at age 18? Assume that the interest is 5% compounded quarterly.

Answer 1

Hi Mir!

To solve this problem we need the discrete compounding interest formula A=P(1+r/n)^(nt) because of the quarterly compounding. In this formula, P is the amount invested, r is the interest rate as a decimal, n is the number of times we are compounding per year, t is the time elapsed in years, and A is the amount of money after time t. Since we are seeking the amount to be invested, we should rearrange the formula to solve for P by dividing both sides by (1+r/n)^(nt), obtaining P=A/(1+r/n)^(nt). Our interest rate as a decimal is 5/100=0.05, so r=0.05. There are four quarters in a year, so n=4. We are going for $55,000 when the son is 18, so t=18 and A=55,000. Plug in the values of r, n, t, and A to get the required initial investment:

P=55,000/(1+0.05/4)^(4*18)=22,486.42 (to the nearest cent)

Therefore the mother needs to invest $22,846.42 to ensure her son has $55,000 by the time he is 18.

I hope this helps!

Answer 2

Use the formula A = P(1 + i)^t, where A = $55,000, i = 0.05 (the interest rate as a decimal), and t = 72 (the number of quarters in 18 years). You are trying to find P. Because the interest is compounded quarterly, the interest rate per period is 0.05/4. Thus, you have the following equation:

55,000 = P(1 + 0.05)⁷²

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