Peter K. answered • 09/24/19

Experienced and Knowledgeable Mathematics and Physics Tutor

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