Annuities Topic Test

Annuities · MST-12-S2-03

Maths Standard Year 12 · All 3 lessons · MC checkpoint plus separate short-answer practice

L1, Annuities L2, Future Value of Annuities L3, Present Value of Annuities
25 MC 8 SA ~55 min
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Complete the 25 multiple choice questions to unlock a sharper next move. The short-answer section below is separate practice.

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Part A, Multiple Choice (1 mark each, 25 marks total)
1 An annuity is best described as: L1
D, a stream of equal payments made at regular intervals. Annuities use regular equal deposits or withdrawals.
2 For $200 deposited monthly for 3 years, the number of payments is: L1
B, $36$. $3 \times 12 = 36$.
3 If interest is 6% p.a. compounded monthly, the monthly rate is: L1
A, $0.005$. $0.06 \div 12 = 0.005$.
4 Future value is used when you want to know: L1
C, what regular deposits grow to in the future. Future value accumulates payments forward.
5 Present value is used when you want to know: L1
B, the lump sum today equivalent to future regular payments. Present value discounts future payments back to today.
6 For ordinary annuity future value, the common formula is: L2
D, $FV = M\dfrac{(1+r)^n-1}{r}$. This is the taught FV formula.
7 For ordinary annuity present value, the common formula is: L3
C, $PV = M\dfrac{1-(1+r)^{-n}}{r}$. This is the taught PV formula.
8 A deposit of $100 per month for 2 years has how many monthly payments? L2
A, $24$. $2 \times 12 = 24$.
9 For $\$100$ per month at monthly rate $0.01$ for 12 months, which setup finds future value? L2
D, $100\dfrac{(1.01)^{12}-1}{0.01}$. Use the FV annuity formula.
10 For $\$500$ per month for 5 years at 6% p.a. compounded monthly, $n$ equals: L3
B, $60$. Five years of monthly payments gives $60$.
11 For a mortgage repayment calculation, the loan amount is usually treated as: L3
A, present value. A loan amount today is the present value of future repayments.
12 If payments are made at the start of each period, the future value is: L2
C, larger. Each payment earns interest for one extra period.
13 At rate $r=0$, $200$ paid monthly for $10$ months has future value: L2
D, $2\,000$. With no interest, total value is $200 \times 10$.
14 A repayment of $300 per month for 4 years has total payments of: L3
A, $14\,400$. There are 48 payments, so $300 \times 48 = 14\,400$.
15 For $M=250$, $r=0.004$, $n=60$, the expression $(1+r)^n$ is: L2
B, $(1.004)^{60}$. Use $1+r = 1.004$ and exponent $60$.
16 Increasing the interest rate while keeping $M$ and $n$ fixed generally makes PV: L3
C, smaller. Higher discount rates reduce present value.
17 If an account target is $\$50\,000$ and you solve for $M$, you are finding: L2
A, the required regular payment. Solving for $M$ gives the regular deposit.
18 If a bank quotes 4.8% p.a. compounded monthly, use monthly rate: L3
D, $0.004$. $0.048 \div 12 = 0.004$.
19 A future value table factor is 39.336. For $M=200$, $FV$ is: L2
B, $7\,867.20$. $200 \times 39.336 = 7\,867.20$.
20 A present value table factor is 51.725 and $M=500$. The present value is: L3
C, $25\,862.50$. $500 \times 51.725 = 25\,862.50$.
21 Which value must match the compounding period? L1
D, The payment period. Rate, periods and payments must use matching units.
22 For a 25-year mortgage with monthly repayments, $n$ is: L3
A, $300$. $25 \times 12 = 300$.
23 If $FV=12\,000$ and annuity factor is 48, then $M$ is: L2
C, $250$. $12\,000 \div 48 = 250$.
24 A present value is less than the total of all future payments mainly because: L3
B, future payments are discounted for interest. Money now can earn interest, so future payments are worth less today.
25 Which is the best first step in an annuity question? L1
D, Identify FV or PV, payment amount, rate per period and number of periods. Correct setup depends on these quantities.
Part B, Short Answer (separate practice)
0 L1
A person deposits $150 per month for 4 years.
(a) Find the number of payments.
(b) State whether this is FV or PV if asked for the amount after 4 years.
(a) $n = 48$.
(b) It is a future value question.
1 L2
Use $FV = M\dfrac{(1+r)^n-1}{r}$ for $M=200$, $r=0.005$, $n=36$.
(a) Substitute values.
(b) Evaluate using $(1.005)^{36} \approx 1.19668$.
(a) $FV = 200\dfrac{(1.005)^{36}-1}{0.005}$.
(b) $FV \approx \$7\,867$.
2 L2
A target savings amount is $30\,000 in 5 years. The FV factor is 67.006.
(a) Find the monthly deposit required.
(b) Explain why rounding up may be sensible.
(a) $M \approx \$447.72$.
(b) Rounding to $448 helps make sure the target is reached.
3 L3
A pension pays $600 per month for 8 years. The PV factor is 77.225.
(a) Find the present value.
(b) Explain the meaning of the answer.
(a) $PV = 600 \times 77.225 = \$46\,335$.
(b) It is the lump sum today equivalent to the payments.
4 L3
Use $PV = M\dfrac{1-(1+r)^{-n}}{r}$ for $M=500$, $r=0.004$, $n=60$.
(a) Substitute into the formula.
(b) Evaluate using $(1.004)^{-60} \approx 0.7870$.
(a) $PV = 500\dfrac{1-(1.004)^{-60}}{0.004}$.
(b) $PV \approx \$26\,625$.
5 L3
A $240\,000 loan is repaid monthly over 20 years with PV factor 151.525.
(a) Find the monthly repayment.
(b) Find the total amount repaid.
(a) $M \approx \$1\,583.90$.
(b) Total $\approx \$380\,136$.
6 L2 & L3
Classify: saving for a car, mortgage repayments, pension withdrawals.
(a) Classify each context.
(b) Give one reason for each classification.
(a) Saving is FV; mortgage and pension withdrawals are PV.
(b) Savings grow forward; loans and pensions value future payments today.
7 L1
An interest rate is 7.2% p.a. compounded monthly.
(a) Convert it to a monthly decimal rate.
(b) Find $n$ for 6 years of monthly payments.
(a) $r = 0.006$.
(b) $n = 72$.
Annuities Complete

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