1. Mr. Kane recently borrowed $15,000 from his Aunt Jemima, and he has promised to pay his aunt $5,000 per year at 15%. How long will it take Mr. Kane to pay off the entire loan from his aunt?
2. You just borrowed $1,000 from Mr. Loan Shark. Mr. Shark requires you to pay $150 per week for the next 10 weeks. What is the effective annual interest rate on this loan?
I figured I'd jump in here relatively shortly after you posted this just so you don't check back a day later and see this question.
What have you done with these questions? Let us know so we know how to help you. Post your work and your solutions or post your question of what you don't understand in there.
To answer these questions, we need to use the formula for calculating the time it takes to pay off a loan with equal annual payments, as well as the formula for calculating the effective interest rate.
1. To calculate how long it will take Mr. Kane to pay off the entire loan from his Aunt Jemima, we can use the formula for the number of periods in an annuity:
n = (log(A/P) / log(1 + r))
Where:
n = number of periods (years in this case)
A = loan amount ($15,000)
P = annual payment ($5,000)
r = interest rate (15% or 0.15)
Plugging in the given values, we have:
n = (log(15000/5000) / log(1 + 0.15))
Using a calculator, we can solve this equation to find the value of 'n', which represents the number of years it will take to pay off the loan.
2. To calculate the effective annual interest rate on the loan from Mr. Loan Shark, we can use the formula for the present value of an annuity:
PV = A * (1 - (1 + r)^(-n)) / r
Where:
PV = present value or loan amount ($1,000)
A = periodic payment ($150)
r = effective interest rate (to be determined)
n = number of periods (weeks in this case, which is 10)
We need to find the value of 'r' by rearranging the formula and solving for 'r'.
r = ((A * n) / PV) - 1
Plugging in the given values, we have:
r = ((150 * 10) / 1000) - 1
Again, using a calculator, we solve the equation to find the value of 'r', which represents the effective annual interest rate on the loan.