Tasks 08-02 - Annuities & Loan Amortization

Section 08: Financial Mathematics

Problem 1: Future Value of Ordinary Annuity (x)

Calculate the future value of each ordinary annuity:

  1. 200 per month for 5 years at 6% annual interest
  2. 500 per month for 10 years at 4% annual interest
  3. 1,000 per quarter for 8 years at 8% annual interest
  4. 3,000 per year for 15 years at 5% annual interest

Problem 2: Present Value of Ordinary Annuity (x)

Calculate the present value of each ordinary annuity:

  1. 400 per month for 4 years at 6% annual interest
  2. 1,500 per month for 20 years at 5% annual interest
  3. 2,000 per quarter for 10 years at 8% annual interest
  4. 5,000 per year for 25 years at 4% annual interest

Problem 3: Finding the Payment (xx)

Find the required payment for each scenario:

  1. Save for 100,000 in 20 years at 5% compounded monthly
  2. Pay off a 30,000 loan in 5 years at 6% compounded monthly
  3. Save for 50,000 in 10 years at 4% compounded quarterly
  4. Pay off a 200,000 mortgage in 30 years at 4.5% compounded monthly

Problem 4: Finding Number of Payments (xx)

How many payments are needed for each scenario?

  1. 15,000 loan at 6% monthly, 350/month payments
  2. 40,000 loan at 4.8% monthly, 800/month payments
  3. Save 75,000 at 5% monthly by saving 400/month

Problem 5: Annuity Due vs. Ordinary Annuity (xx)

For each scenario, calculate both the ordinary annuity and annuity due values:

  1. FV of 500/month for 10 years at 6%
  2. PV of 1,000/month for 5 years at 4%

Problem 6: Loan Payment Calculation (x)

Calculate the monthly payment for each loan:

  1. 20,000 car loan at 5.5% for 4 years
  2. 150,000 mortgage at 4.2% for 25 years
  3. 8,000 personal loan at 9% for 3 years
  4. 35,000 business loan at 6.5% for 7 years

Problem 7: Amortization Schedule (xxx)

Create the first 4 rows of an amortization schedule for a 12,000 loan at 6% annual interest for 2 years (monthly payments).

Payment # Payment Interest Principal Balance
0 - - - ?
1 ? ? ? ?
2 ? ? ? ?
3 ? ? ? ?
4 ? ? ? ?

Problem 8: Outstanding Balance (xx)

For a 180,000 mortgage at 4.8% annual for 30 years (monthly payments):

  1. Calculate the monthly payment.
  2. Find the outstanding balance after 5 years (60 payments).
  3. Find the outstanding balance after 15 years (180 payments).
  4. How much total interest is paid over the life of the loan?

Problem 9: Retirement Planning (xxx)

Maria wants to retire with 800,000 Euro in her retirement account. She’s 30 years old and plans to retire at 65.

  1. If her account earns 6% compounded monthly, how much must she save monthly?
  2. If she can only save 500/month, what rate of return does she need?
  3. If she delays starting by 5 years (starts at 35), how much more per month must she save at 6%?

Problem 10: Comparing Loan Options (xxx)

You need to borrow 25,000 for a car. Compare these options:

Option A: 4.9% APR for 48 months Option B: 3.9% APR for 60 months Option C: 0% APR for 36 months (but 1,000 rebate lost)

  1. Calculate the monthly payment for each option.
  2. Calculate the total cost (payments minus any rebate) for each.
  3. Which option is best financially?

Problem 11: Business Equipment Lease (xxx)

A company needs equipment worth 80,000. They can either:

  • Buy: Pay 80,000 now
  • Lease: Pay 1,800/month for 4 years, then return the equipment

At a 5% discount rate:

  1. What is the present value of the lease payments?
  2. If the equipment has a resale value of 15,000 after 4 years, which option is better?
  3. At what resale value would the two options be equivalent?

Problem 12: Mixed Annuity Problem (xxxx)

The Muller family is planning for their child’s education. They start saving when their child is born and need 150,000 when the child turns 18.

  1. If they save monthly at 5% annual return, what monthly payment is needed?
  2. After 10 years of saving, how much have they accumulated?
  3. At that point (child is 10), they receive an inheritance of 40,000 and add it to the account. What is their new required monthly payment for the remaining 8 years?
  4. Alternatively, if they keep the same payment from part (a), how much extra will they have at age 18?