Financial applications: compound interest, depreciation, loans and annuities

Maths: Applications and Interpretation · Number and algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

With compound interest, interest is added to the balance and then earns interest itself, so the value grows geometrically. A nominal annual rate is shared equally between the compounding periods: 6% compounded monthly means 0.5% each month. Depreciation uses the same formula with a negative rate.

Loans and annuities involve a regular payment as well. These are done with the finance (TVM) solver on your calculator. Enter what you know and solve for the missing value. Money you pay out and money you receive must have opposite signs.

Inflation reduces what money can buy. The real value of an investment is found using a rate lowered by the inflation rate.

Rules to remember

Compound interest: FV = PV × (1 + r/(100k))^kn, with r = nominal annual rate in %, k = compounding periods per year, n = years
k = 1 yearly, 2 half-yearly, 4 quarterly, 12 monthly
Depreciation at r% per year: value = PV × (1 − r/100)ⁿ
TVM solver: N = number of payments, I% = nominal annual rate, PV, PMT, FV, P/Y and C/Y = payments and compounding periods per year
Loan fully repaid: FV = 0. Savings annuity starting from nothing: PV = 0
total interest on a loan = payment × number of payments − amount borrowed
Real value: use real rate ≈ interest rate − inflation rate, then apply the compound interest formula

Common mistake

Students compound monthly but forget to change both numbers: the rate must be divided by 12 and the number of periods multiplied by 12. In the TVM solver, N is the number of payments, not the number of years.

Worked example

$6000 is invested at a nominal annual rate of 4.8%, compounded quarterly. Find its value after 3 years, to the nearest dollar.

Quarterly means k = 4, so the rate per period is 4.8% ÷ 4 = 1.2% and the number of periods is 4 × 3 = 12.
FV = 6000 × (1 + 0.012)¹² = 6000 × 1.012¹².
1.012¹² = 1.15389..., so FV = 6000 × 1.15389... = 6923.37.

Answer: $6923 to the nearest dollar

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Topic 1: Number and Algebra

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