Jeremiah is going to take out a $6,000 loan to buy a new jet ski. The bank he is taking the loan out will charge him a 6% interest rate that is compounded annually. He can either pay the loan back in 3 years or 4 years. How much more interest will he pay if he takes the loan out for 4 years?
To calculate the total interest paid for a loan compounded annually, you can use the formula:
Total Interest = Principal * (1 + r)^n - Principal,
where:
- Principal = $6,000
- r = 6% or 0.06
- n = number of years
For a 3-year loan:
Total Interest = $6,000 * (1 + 0.06)^3 - $6,000
Total Interest = $6,000 * (1.191016) - $6,000
Total Interest = $7140.096 - $6,000
Total Interest = $1,140.096
For a 4-year loan:
Total Interest = $6,000 * (1 + 0.06)^4 - $6,000
Total Interest = $6,000 * (1.262476) - $6,000
Total Interest = $7574.856 - $6,000
Total Interest = $1,574.856
Therefore, Jeremiah will pay $1,574.856 - $1,140.096 = $434.76 more interest if he takes the loan out for 4 years.