Annuities & Loan Repayments (Grade 12) — Worksheet & Memo

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Grade 12 · Finance, Growth and Decay

Annuities & Loan Repayments (Grade 12)

MEMORANDUM

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Date:

Mark

/ 34

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
R1 500 is deposited monthly for 20 years at 9% p.a. compounded monthly. Determine the future value.
(3)
i = 0,0075, n = 240 → F = R1 001 830,30✓✓✓ (3)
2
How much was actually deposited in total in that annuity?
(2)
240 × 1 500 = R360 000✓✓ (2)
3
A bond of R800 000 is repaid monthly over 20 years at 9% p.a. compounded monthly. Determine the monthly instalment.
(4)
x = (800 000 × 0,0075)/(1 − (1,0075)⁻²⁴⁰) = R7 197,81✓✓✓✓ (4)
4
Determine the outstanding balance on that bond after 5 years.
(4)
240 − 60 = 180 payments remain ✓; Balance = (7 197,81[1 − (1,0075)⁻¹⁸⁰])/0,0075 ✓✓ = R709 656,62 ✓ (R709 656,39 with the unrounded instalment)(4)
5
Write down the value of i for 9% p.a. compounded monthly.
(1)
0,09/12 = 0,0075✓ (1)
6
Which formula do you use when saving towards a future amount?
(1)
Future value, F = (x[(1 + i)ⁿ − 1])/i✓ (1)
7
Which formula do you use for a loan taken out today?
(1)
Present value, P = (x[1 − (1 + i)⁻ⁿ])/i✓ (1)
8
How is the outstanding balance on a loan calculated?
(2)
As the present value of the payments still outstanding.✓✓ (2)
9
How long will it take R20 000 to double at 8% p.a. compounded annually? Give your answer in whole years.
(4)
40 000 = 20 000(1,08)ⁿ ✓; (1,08)ⁿ = 2 ✓; n = (log 2)/(log 1,08) = 9,006 ✓; so 10 years (interest is only added at year end) ✓(4)
10
A vehicle costing R450 000 depreciates at 15% p.a. on a reducing balance. Calculate its scrap value after 4 years.
(3)
450 000(1 − 0,15)⁴ ✓✓ = R234 902,81 ✓(3)
11
In a sinking-fund question, state the THREE amounts you must calculate before working out the monthly payment.
(3)
The scrap value of the old asset ✓; the inflated cost of the new one ✓; and the difference between them, which is what the fund must produce ✓(3)
12
Option A pays 9,6% p.a. compounded monthly; Option B pays 9,9% p.a. compounded annually. Which is better? Show your reasoning.
(4)
A effective = (1 + 0,096/12)¹² − 1 ✓ = 0,10034 = 10,03% ✓; B = 9,9% ✓; Option A is better because its effective annual rate is higher ✓(4)
13
Why can a loan with a lower monthly instalment cost you more overall?
(2)
A lower instalment usually means a longer term ✓, so interest is charged for more months and the total repaid is larger ✓(2)

TOTAL: 34 marks