Mmisi borrows an amount of money from Aggie. After two years, Mmasi pays back the money, plus \( 18 \% \) simple interest per year. He has to pay back an amount of R4080. How moch moncy did he borrow from Aggie? Nelis invests R 3000 for 5 years. He ends up with R4500. What was the simple interest rate? Ettiene wants to lonow for how long he needs to invest his R2 000 at \( 15 \% \) p-a. simple interest in order to have RI1 000. Answer Ertiene's question. Jurgen wants to buy a tumblo dryer for R1 500 . He cannot afford to pay all at once, so he buys it on hire purchasc. According to the agreement, he will pay back the money, plus \( 12 \% \) simple interest per year, by means of monthly payments, over a two-year period. (1) Calculate the total amount of money he'Il have to pay. (7) Caleulate hie menthis narvment
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To find out how much Mmasi borrowed, we can use the formula for simple interest: \( A = P(1 + rt) \). Here, \( A \) is the total amount repayable (R4080), \( P \) is the principal amount borrowed, \( r \) is the rate of interest (0.18), and \( t \) is the time in years (2). Rearranging the formula gives us \( P = \frac{A}{(1 + rt)} = \frac{4080}{(1 + 0.18 \times 2)} = \frac{4080}{1.36} = R3000 \). For Nelis's investment, we can again use the simple interest formula, rearranging it to find the interest rate. We know the initial amount (R3000), the final amount (R4500), and the time (5 years). The total interest earned can be calculated as \( 4500 - 3000 = R1500 \). Using the formula \( I = P \times r \times t \), we get \( 1500 = 3000 \times r \times 5 \), leading to \( r = \frac{1500}{15000} = 0.1 \) or 10% per annum. Now, for Ettiene's investment, we need to determine how long he must invest R2000 at 15% p.a. to reach R11000. Using the formula \( A = P(1 + rt) \), we can rearrange it to find \( t \): \( 11000 = 2000(1 + 0.15t) \). Simplifying gives \( 5.5 = 1 + 0.15t \), so \( 0.15t = 4.5 \), and \( t = 30 \) years. Finally, for Jurgen's tumble dryer purchase, to calculate the total amount he will have to pay under the hire purchase agreement, we first find the interest using the simple interest formula. The principal is R1500, the rate is 12%, and the time is 2 years. Thus, \( I = 1500 \times 0.12 \times 2 = R360 \). Therefore, the total amount he will pay is \( 1500 + 360 = R1860 \). To find his monthly payment, we need to divide this total by the number of months in two years (24 months): \( 1860 ÷ 24 = R77.50 \) per month.
