Asked by Jendayi Campbell on May 13, 2024
Verified
A bank has agreed to loan you $10,000 at 11% for 5 years. You are required to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. Determine the amount of these annual payments (to the nearest dollar) .
A) $2,000
B) $3,100
C) $2,706
D) $1,100
Principal
Principal refers to the original sum of money borrowed in a loan or invested, exclusive of any interest or dividends.
Annual Payments
Periodic payments made once every year, often used in terms of loans, insurance, and investments.
Outstanding Balance
The amount of money owed on a loan or credit line that has not yet been repaid.
- Ascertain and dissect the lucrative and adverse aspects of loan procurement, incorporating the calculation of the total interest expenditure over the span of the loan.
- Understand and calculate payment amounts for mortgages, loans, and annuities, including extra payment scenarios.
Verified Answer
CY
Chazyah YisraelMay 20, 2024
Final Answer :
C
Explanation :
To calculate the annual payment, we can use the formula for the present value of an annuity:
PMT = PV * (r / (1 - (1 + r)^-n))
Where:
PMT = Annual payment
PV = Loan amount = $10,000
r = Annual interest rate = 11% = 0.11
n = Number of payments = 5
Substituting the values, we get:
PMT = 10,000 * (0.11 / (1 - (1 + 0.11)^-5))
PMT = $2,706.49
Rounding to the nearest dollar gives us choice C, $2,706.
PMT = PV * (r / (1 - (1 + r)^-n))
Where:
PMT = Annual payment
PV = Loan amount = $10,000
r = Annual interest rate = 11% = 0.11
n = Number of payments = 5
Substituting the values, we get:
PMT = 10,000 * (0.11 / (1 - (1 + 0.11)^-5))
PMT = $2,706.49
Rounding to the nearest dollar gives us choice C, $2,706.
Learning Objectives
- Ascertain and dissect the lucrative and adverse aspects of loan procurement, incorporating the calculation of the total interest expenditure over the span of the loan.
- Understand and calculate payment amounts for mortgages, loans, and annuities, including extra payment scenarios.