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Applied Math
Grade 10-12
Math of Finance (Loans & Annuities) Cheat Sheet
A printable reference covering simple interest, compound interest, loan payments, annuities, present value, and future value for grades 10-12.
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Math of finance helps students understand how money grows, how loans are repaid, and how regular payments build savings over time. This cheat sheet focuses on loans and annuities, which are common in car loans, mortgages, retirement plans, and savings accounts. Students need these formulas to compare financial choices and understand the cost of borrowing or the value of saving.
Key Facts
- Simple interest is calculated by I = Prt, where P is principal, r is annual interest rate as a decimal, and t is time in years.
- Compound amount is calculated by A = P(1 + r/n)^(nt), where n is the number of compounding periods per year.
- The future value of an ordinary annuity is FV = PMT[((1 + i)^n - 1) / i], where payments are made at the end of each period.
- The present value of an ordinary annuity is PV = PMT[1 - (1 + i)^(-n)] / i.
- A loan payment for an amortized loan is PMT = PV[i / (1 - (1 + i)^(-n))].
- The periodic interest rate is i = annual rate / payments per year, and the number of payments is n = years × payments per year.
- Total interest paid on a loan equals total payments minus principal, or Interest = PMT × n - PV.
- For the same annual rate, more frequent compounding usually produces a higher final amount because interest is added more often.
Vocabulary
- Principal
- The original amount of money borrowed, invested, or deposited before interest is added.
- Interest
- The cost of borrowing money or the earnings from investing money.
- Compound Interest
- Interest calculated on both the original principal and previously earned interest.
- Annuity
- A series of equal payments made at regular time intervals.
- Present Value
- The current worth of a future payment or series of payments, discounted by interest.
- Amortized Loan
- A loan repaid with regular equal payments that cover both interest and part of the principal.
Common Mistakes to Avoid
- Using the percent instead of the decimal rate is wrong because formulas require 6% to be written as 0.06.
- Forgetting to match the rate and payment period is wrong because monthly payments need a monthly interest rate, not the annual rate.
- Using the future value annuity formula for a loan is wrong because a loan payment formula is based on present value and repayment of debt.
- Mixing up n and t is wrong because t is time in years while n is the total number of payment or compounding periods.
- Ignoring total interest paid is wrong because a smaller monthly payment can still cost more overall if the loan lasts longer.
Practice Questions
- 1 Find the simple interest on $2,500 invested at 4.8% per year for 3 years.
- 2 A $1,200 deposit earns 5% annual interest compounded monthly for 4 years. What is the final amount?
- 3 A car loan has a present value of $18,000, a monthly interest rate of 0.005, and 60 monthly payments. Use PMT = PV[i / (1 - (1 + i)^(-n))] to find the monthly payment.
- 4 Explain why two loans with the same interest rate and principal can have different total interest costs.