Annuity and Loan Amortization Questions with Solutions

An annuity is a financial product that pays out a fixed amount of money at regular intervals. A loan amortization schedule shows the breakdown of each periodic payment made towards a loan, including the principal and interest. Here are some annuity and loan amortization questions with solutions:

Question 1: What is the present value of an annuity that pays $1,000 per year for 5 years, assuming a 5% interest rate?

Solution:
Step 1: Determine the present value factor using the formula PVIFA = (1 - (1 + r)^-n) / r, where r is the interest rate and n is the number of periods.
PVIFA = (1 - (1 + 0.05)^-5) / 0.05
PVIFA = 4.32948

Step 2: Multiply the present value factor by the annual payment to get the present value.
Present Value = PVIFA x Annual Payment
Present Value = 4.32948 x $1,000
Present Value = $4,329.48

Therefore, the present value of the annuity is $4,329.48.

Question 2: What is the monthly payment for a $10,000 loan with a 5% interest rate over 3 years?

Solution:
Step 1: Determine the monthly interest rate by dividing the annual interest rate by 12.
Monthly Interest Rate = 5% / 12
Monthly Interest Rate = 0.004167

Step 2: Determine the number of payments by multiplying the number of years by 12.
Number of Payments = 3 x 12
Number of Payments = 36

Step 3: Determine the monthly payment using the formula PMT = (P x r) / (1 - (1 + r)^-n), where P is the loan amount, r is the monthly interest rate, and n is the number of payments.
PMT = (10,000 x 0.004167) / (1 - (1 + 0.004167)^-36)
PMT = $295.24

Therefore, the monthly payment for the loan is $295.24.

Question 3: What is the total interest paid on a $5,000 loan with a 6% interest rate over 4 years, using a loan amortization schedule?

Solution:
Step 1: Create a loan amortization schedule using the formula PMT = (P x r) / (1 - (1 + r)^-n), where P is the loan amount, r is the monthly interest rate, and n is the number of payments.

Month Payment Interest Principal Balance
1 $121.33 $25.00 $96.33 $4,903.67
2 $121.33 $24.52 $96.81 $4,806.86
3 $121.33 $24.05 $97.28 $4,709.58
... ... ... ... ...
47 $121.33 $5.14 $116.19 $257.06
48 $121.33 $2.57 $118.76 $138.30
49 $121.33 $0.00 $121