Compound Interest, Worked Solution

Unit 4 · Loans, Investments and Annuities

Question
A = P(1 + i)n
A = final amount ($)
P = principal (starting amount)
i = interest rate per period
n = number of periods

Mia invests $4 000 in a savings account that earns 6% per annum, compounded monthly, for 3 years.

$4 000Principal (P)
6% p.a.Annual rate
monthlyCompounding
3 yearsTime
🔍 Find the total value of the investment after 3 years.
Worked Solution
1

Identify the interest rate per period (i)

The rate is 6% per year, but interest is added monthly, so divide by 12:

i = 6% ÷ 12 = 0.5% per month
i = 0.005    (always convert % → decimal)
⚠️ Common mistake: Using i = 0.06 instead of 0.005, always divide the annual rate by the number of compounding periods per year.
2

Find the number of periods (n)

Compounded monthly for 3 years, so n = months total:

n = 3 years × 12 months/year = 36 periods
Time line (months)
Month 0
$4 000 12 24 Month 36
A = ?
3

Substitute all values into A = P(1 + i)n

P
=
4 000
i
=
0.005
n
=
36
A
=
?
A = 4 000 × (1 + 0.005)36
A = 4 000 × (1.005)36
4

Evaluate (use your calculator)

(1.005)36 = 1.19668…
A = 4 000 × 1.19668…
A = $4 786.73 (rounded to nearest cent)
💡 Calculator tip: Type: 4000 × 1.005 ^ 36 =
Or use the formula template on your formula sheet.
5

Find interest earned (bonus)

Interest = A − P
Interest = $4 786.73 − $4 000
Interest = $786.73
Value after 3 years
A = $4 786.73
✓
Quick Reference, Compounding Periods
Compounded… Periods per year Divide rate by n = years ×
Annually 1 ÷ 1 × 1
Quarterly 4 ÷ 4 × 4
Monthly 12 ÷ 12 × 12
Weekly 52 ÷ 52 × 52
Now you try!, same method, different numbers
Practice A
$8 000 invested at 4.8% p.a.,
compounded quarterly for 5 years.

Find A.
i = 0.012, n = 20 → A ≈ $10 210.08
Practice B
$12 500 invested at 3% p.a.,
compounded annually for 4 years.

Find the interest earned.
A ≈ $14 067.55 → Interest ≈ $1 567.55