Browse · MATH
Printjmc
algebra senior
Problem
Luke is borrowing \10{,}00010{\bf Plan~1.}10\%510{\bf Plan~2.}10\%10$ years.
What is the (positive) difference between Luke's total payments under Plan 1 and his total payments under Plan 2? Round to the nearest dollar.
What is the (positive) difference between Luke's total payments under Plan 1 and his total payments under Plan 2? Round to the nearest dollar.
Solution
For Plan 1, we use the formula , where is the end balance, is the principal, is the interest rate, is the number of years, and is the number of times compounded in a year.
First we find out how much he would owe in years. He pays off half of it in years, which is \frac{\16,\!386.16}{2}=\ He has \8,\!193.085\8,\!193.08+\13,\!425.32=\ in ten years if he chooses Plan 1.
With Plan 2, he would have to pay \10,000\left(1+0.1\right)^{10} \approx \ in years.
Therefore, he should choose Plan 1 and save .
First we find out how much he would owe in years. He pays off half of it in years, which is \frac{\16,\!386.16}{2}=\ He has \8,\!193.085\8,\!193.08+\13,\!425.32=\ in ten years if he chooses Plan 1.
With Plan 2, he would have to pay \10,000\left(1+0.1\right)^{10} \approx \ in years.
Therefore, he should choose Plan 1 and save .
Final answer
4319 \text{ dollars}