Grade 12 · Question 5 · NSC Exam Style
Grade 12 — Finance, Growth & Decay Quiz | Maths Maestri draws its questions at random from 5 questions across these topics:
A few of the question types, with full solutions, so you know what to expect.
Depreciation (Reducing Balance). Dumisani buys a truck for R650 000. It depreciates at 30% per annum on the reducing balance method. Calculate the depreciated value of the truck after 4 years.
Answer: R156 065
Reducing balance formula: \(A = P(1 - i)^n\) \(A = 650\,000(1 - 0{,}30)^{4}\) \(A = 650\,000 \times (0{,}70)^{4}\) \(A = 650\,000 \times 0{,}2401\) !\(A = \text{R}156\,065\)
Appreciation (Inflation). The price of a new truck appreciates, as a result of inflation, at a rate of 15% per annum. The current price of a new truck is R650 000. Calculate the value of a new truck in 4 years' time.
Answer: R1 136 854,06
Compound growth: \(A = P(1 + i)^n\) \(A = 650\,000(1 + 0{,}15)^{4}\) \(A = 650\,000 \times (1{,}15)^{4}\) \(A = 650\,000 \times 1{,}74900625\) !\(A = \text{R}1\,136\,854{,}06\)
Sinking Fund. Dumisani plans to replace the original truck in 4 years' time. He will use the current truck as a trade-in (worth R156 065) and pay the remaining amount in cash via a sinking fund. The sinking fund earns 9,5% per annum, compounded monthly. The first instalment is paid at the end of the first month of the 4-year period and the last instalment is made at the end of the 4 years. Calculate the monthly instalment Dumisani pays into the sinking fund.
Answer: R16 875,92
Cash required = New price \(-\) Trade-in value \(= 1\,136\,854{,}06 - 156\,065 = \text{R}980\,789{,}06\) Future value annuity: \(F = \dfrac{x\left[\left(1 + i\right)^n - 1\right]}{i}\) \(i = \dfrac{0{,}095}{12}\), \(n = 4 \times 12 = 48\) \(980\,789{,}06 = \dfrac{x\left[\left(1 + \dfrac{0{,}095}{12}\right)^{48} - 1\right]}{\dfrac{0{,}095}{12}}\) !\(x = \text{R}16\,875{,}92\)
Loan — Outstanding Balance. Harry buys a property for R1 500 000. After paying a deposit, he takes a loan for the remaining amount of R1 275 000, at an interest rate of 9,2% per annum, compounded monthly over a period of 20 years. The monthly instalment on the loan is R11 636,02. Calculate the outstanding balance of the loan after 7 years.
Answer: R1 056 675,39
Outstanding balance after 84 months: \(OB = P\left(1 + \dfrac{i}{12}\right)^{n} - \dfrac{x\left[\left(1 + \dfrac{i}{12}\right)^{n} - 1\right]}{\dfrac{i}{12}}\) \(i = 0{,}092,\ n = 7 \times 12 = 84,\ x = 11\,636{,}02\) \(OB = 1\,275\,000\left(1 + \dfrac{0{,}092}{12}\right)^{84} - \dfrac{11\,636{,}02\left[\left(1 + \dfrac{0{,}092}{12}\right)^{84} - 1\right]}{\dfrac{0{,}092}{12}}\) !\(OB = \text{R}1\,056\,675{,}39\)
Loan — Revised Instalment. After 7 years, due to financial difficulty, Harry misses 5 consecutive payments. Thereafter he continues making monthly payments into the loan account until the end of the 20-year period. Calculate the value of the new monthly instalment to settle the loan.
Answer: R12 297,82
Step 1 — Balance grows for 5 missed months: \(B = 1\,056\,675{,}39\left(1 + \dfrac{0{,}092}{12}\right)^{5} = \text{R}1\,097\,807{,}15\) Step 2 — Remaining months after missing 5: \(n = 240 - 84 - 5 = 151 \text{ months}\) Step 3 — Present value annuity: \(1\,097\,807{,}15 = \dfrac{x\left[1 - \left(1 + \dfrac{0{,}092}{12}\right)^{-151}\right]}{\dfrac{0{,}092}{12}}\) !\(x = \text{R}12\,297{,}82\)