Compounded interest quaterly and continuously, Investing, Business

Question

Having received a large inheritance, Jing-mei's parents wish to establish a trust for her college education. Seven years from now they need an estimated $130,000. How much should they set aside in trust now if they invest the money at 5.7%/year compounded quarterly? Continuously? (Round your answers to the nearest cent.)

Quarterly $_____

Continuously $_____

This problem really confused me. I didnt know how to finish the problem. Thank you for any help!

Answer 1

Let's start with the formula for compound interest.

A = P(1 + r/n)^nt

Where A is the total amount of money you will have after interest is added (i.e. $130,000), P is the principal amount you invest (i.e. this is what we are actually looking for), r is the yearly interest rate (i.e. 5.7 %), n is the number of times the principal amount is compounded per year (i.e. 4 times), and t is the number of years that the money will be in the accruing interest (i.e. 7 years). We want to rearrange the above equation to solve for the principal amount P and plug in these values:

P = A / (1+r/n)^nt

= ($ 130,000) / (1 + (0.057/4))⁽⁴⁾⁽⁷⁾

= ($ 130,000) / (1 + 0.01425)²⁸

= ($ 130,000) / (1.01425)²⁸

= $ 87,474.79