Key Idea: An annuity is a series of equal, regular payments. Topic 1.7 is entirely GDC-based — you use the TVM (Time Value of Money) solver on your GDC. You enter what you know and solve for the unknown. The two main scenarios are: saving (money in) and borrowing (money out).
✏️ Worked examples
Savings annuity — find FV
Save $200/month for 5 years at 4% annual interest compounded monthly.
Step by step:
N = 5 × 12 = 60, I% = 4, PV = 0, PMT = −200, P/Y = 12, C/Y = 12
Solve for FV
GDC → FV = $13 259.80
FV = $13 259.80
🔒 GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Loan — find monthly payment
Borrow $10 000 at 6% annual interest, repaid monthly over 3 years.
Step by step:
N = 36, I% = 6, PV = 10 000, FV = 0, P/Y = 12, C/Y = 12
Solve for PMT
GDC → PMT = −$304.22 (negative = paying out)
$304.22 per month
🔒 GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Loan — find total interest
Same loan as above. Find the total interest paid over the full term.
Step by step:
Total paid = |PMT| × N = 304.22 × 36 = $10 951.92
Interest = total paid − principal = 10 951.92 − 10 000
Total interest = $951.92
$951.92 in interest
Always list TVM inputs — write down N, I%, PV, PMT, FV, P/Y, C/Y before stating your answer. This is your working. No inputs shown = no method marks. Currency: Round final answers to 2 decimal places unless told otherwise. Common question types: monthly payment, number of months to repay, total interest paid, comparing two loan options. This topic is Paper 2 only — you will always have your GDC.
IB-style question [6 marks]
Ravi wants to buy a van priced at $24 000. He pays a deposit of $4 000 and borrows the rest from a bank. The loan has a nominal annual interest rate of 8.4%, compounded monthly, and is repaid in equal instalments at the end of each month over 4 years. (a) Write down the amount Ravi borrows. (b) Find the monthly repayment, correct to the nearest dollar. (c) Find the total interest Ravi pays over the 4 years.
Step by step:
(a) Subtract the deposit from the price. This is a write-down — no TVM needed.
(b) Set up the TVM solver. Monthly for 4 years gives N = 4 × 12; Ravi receives the loan so PV is positive, and FV = 0.
Solve for PMT and round to the nearest dollar.
(c) Total paid = repayment × number of months, then subtract the amount borrowed.
(a) $20 000 borrowed. (b) $492 per month. (c) About $3617 in interest.