Question

Micah needs $18,500 to purchase a boat. How much money will he need to invest today in a savings account earning 3.2% interest, compounding quarterly, to have enough money to purchase the boat in 14 years?

Answer 1

We have that every quarter, he will get an 0.8% interest rate. We also have that there will be 14*4=56 periods of repayment. We have that by the formula, if there are n periods and x% is the interest rate, the capital is multiplied by (100+x%)^n.
Suppose Micah invests x money. Then, we have that after 14 years, the capital available will be C=$x*(1.008)^{56}=x*1.562$. We have that C=18500$ and hence that 18500=x*1.562. Thus, solving for x we have that x=11841$.
Micah will need to invest only 11841$ in order to pay for his boat; this shows the importance of saving since he earns a lot of money, around 7k $.