2. Present Value of a Lump Sum You want to have \( \$ 50,000 \) in your account 15 years from now. If the annual discount rate is \( 6 \% \), how much should you invest today? Assume annual compounding.

121. A shopkeeper advertises for selling cloth at \( 4 \% \) loss. However, by using a false metre scale he actually gains \( 20 \% \). What is the actual length of the scale? \( \begin{array}{ll}\text { (R.R.B., } 2006 \text { ) } \\ \begin{array}{ll}\text { (a) } 70 \mathrm{~cm} & \text { (b) } 75 \mathrm{~cm} \\ \text { (c) } 80 \mathrm{~cm} & \text { (d) } 90 \mathrm{~cm}\end{array} \\ \text { 122. Instead of a metre scale, a cloth merchant uses a } \\ 120 \mathrm{~cm} \text { scale while buying but uses an } 80 \mathrm{~cm} \text { scale } \\ \text { while selling the same cloth. If he offers a discount } \\ \text { of } 20 \% \text { on cash payment what is his overall profit } \\ \text { percentage? } \\ \begin{array}{ll}\text { (a) } 15 \% & \text { (b) } 20 \% \\ \text { (c) } 25 \% & \text { (d) } 40 \%\end{array} \\ \text { gain percentage but actually earns } 37 \frac{1}{2} \% \text { profit by } \\ \text { using false weight. If for a kg he uses a weight of } \\ 800 \text { gm, what is the nominal gain percentage at } \\ \text { which he claims to be selling his goods? } \\ \begin{array}{ll}\text { (a) } 8 \% & \text { (b) } 10 \% \\ \text { (c) } 15 \% & \text { (d) } 20 \%\end{array}\end{array} \).

QUESTION 2 Boitumelo invests an amount of R28 000 for a period of 7 years. For the first two years the interest was \( 12 \% \) p.a. compounded semi-annually. The interest was then changed to \( 10 \% \) p.a. compounded quarterly. Determine the value of the investment after the 7 -year period. \( 2.2 \quad \begin{array}{l}\text { Convert an interest rate of } 10 \% \text { p.a. compounded quarterly to an annual effective (3) } \\ \text { interest rate. }\end{array} \) \( 2.3 \quad \begin{array}{l}\text { A lawnmower was traded in for R236 after } 10 \text { years. The depreciation was } \\ \text { calculated at } 9.2 \% \text { p.a. on a straight-line basis. } \\ \text { Determine the cost of the lawnmower } 10 \text { years ago. }\end{array} \)

A, B को 600 रु. 2 वर्बों के लिए वर्षो के लिए उधार देता है तथा A' दोनों से एक साथ 90 रु. साधारण ब्यांज के रूप में प्राप्त करता है। ब्याज की दर ज्ञात करें। \( \begin{array}{ll}\text { (1) } 5 \% & \text { (2) } 3 \% \\ \text { (3) } 6 \% & \text { (4) } 7 \%\end{array} \) क निक्नित धन को साधारण ब्याज की एक निश्चित दत

Boitumelo invests an amount of R28 000 for a period of 7 years. For the first two (3) years the interest was \( 12 \% \) p.a. compounded semi-annually. The interest was then changed to \( 10 \% \) p.a. compounded quarterly. Determine the value of the investment after the 7 -year period.

8. The rule \( V_{n}=6000 \times 1.09^{n} \) could be used to model which of the following scenarios? A. An investment of \( \$ 6000 \) with an interest rate of \( 0.09 \% \) p.a, compounding monthly. B. An investment of \( \$ 6000 \) with an interest rate of \( 0.09 \% \) p.a, compounding quarterly. C. An investment of \( \$ 6000 \) with an interest rate of \( 9 \% \) p.a, compounding monthly. D. An investment of \( \$ 6000 \) with an interest rate of \( 9 \% \) p.a, compounding annually. 9. Find the final value of each of the following investments, compounding yearly, correct to the nearest cent. a. \( \$ 120 \) invested for three years with compound interest of \( 5 \% \) per annum. b. \( \$ 9000000 \) invested in a compound interest account for five years at \( 8.2 \% \) per annum. c. \( \$ 230000 \) invested in a compound interest account for twenty years at \( 2.31 \% \) per annum.