Thando has R4 500 in his savings account. The bank pays him a compound interest rate of 4.25% p.a. Calculate the amount Thando will receive if he decides to withdraw the money after 30 months.
The following advertisement appeared with regard to buying a bicycle on a hire-purchase agreement loan:
Purchase price: R 5989
Required deposit: R 600
Loan rest?: Only 18 months, at 8% pa, simple interest
4.2.1 Calculate the monthly amount that a person has to budget for in order to pay for the bicycle.
4.2.2 How much interest does one have to pay over the full term of the loan?
The following information is given:
1 ounce = 28.35 g
$1 = R 8.79
Calculate the rand value of a 1 kg gold bar, if 1 ounce of gold is worth $978.34.
Answer (2)
Calculate the amount Thando receives using compound interest: A = 4500 ( 1 + 0.0425 ) 2.5 = R 4993.47 .
Determine the monthly bicycle payment: Loan amount is 5989 − 600 = R 5389 , interest is 5389 × 0.08 × 1.5 = R 646.68 , so monthly payment is ( 5389 + 646.68 ) /18 = R 335.32 .
Find the total interest on the bicycle loan: R 646.68 .
Compute the rand value of a 1 kg gold bar: ( 1000/28.35 ) × 3978.34 × 8.79 = R 1233495.89 .
The amount Thando will receive is R 4993.47 , the monthly bicycle payment is R 335.32 , the total interest on the bicycle loan is R 646.68 , and the rand value of a 1 kg gold bar is R 1233495.89 .
Explanation
Calculating Compound Interest First, let's calculate the amount Thando will receive after 30 months. We use the compound interest formula: A = P ( 1 + r ) t , where P is the principal amount, r is the annual interest rate, and t is the time in years. Here, P = R 4500 , r = 4.25% = 0.0425 , and t = 30/12 = 2.5 years. Therefore, A = 4500 ( 1 + 0.0425 ) 2.5 . The result of this calculation is R 4993.47 .
Calculating Monthly Bicycle Payment Next, we calculate the monthly amount for the bicycle. The purchase price is R 5989 and the deposit is R 600 , so the loan amount is 5989 − 600 = R 5389 . The simple interest rate is 8% per annum, and the loan term is 18 months (1.5 years). The total interest paid is I = PRT = 5389 × 0.08 × 1.5 = R 646.68 . The total amount to be paid back is 5389 + 646.68 = R 6035.68 . The monthly payment is 6035.68/18 = R 335.32 .
Calculating Total Interest on Bicycle Loan The total interest paid over the full term of the bicycle loan is R 646.68 , as calculated in the previous step.
Calculating Rand Value of Gold Bar Finally, we calculate the rand value of a 1 kg gold bar. We know that 1 ounce = 28.35 g, so 1 kg = 1000 g = 1000/28.35 ounces. 1 ounce of gold is worth $3978.34 , and $1 = R 8.79 . Therefore, the value of 1 kg of gold in Rands is ( 1000/28.35 ) × 3978.34 × 8.79 = R 1233495.89 .
Final Answers In conclusion, Thando will receive R 4993.47 after 30 months. The monthly payment for the bicycle is R 335.32 . The total interest paid for the bicycle loan is R 646.68 . The rand value of a 1 kg gold bar is R 1233495.89 .
Examples
These calculations are useful in everyday financial planning. Understanding compound interest helps in making informed decisions about savings and investments. Calculating loan payments and interest is crucial when considering financing options for purchases. Converting currency and understanding the value of precious metals are important in international trade and investment.
Thando will receive approximately R4993.47 from his savings after 30 months. The monthly payment for the bicycle will be about R335.32, with a total interest of R646.68 on the loan. The rand value of a 1 kg gold bar is about R1233495.89.
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