QQuestionMathematics
QuestionMathematics
Interest is paid at 8.6% p.a, compounding monthly, on an investment of K^20 000.
A) how much interest has been credited to the account after the first year?
B) how much is in the account after 3 years?
C) what rate of simple interest per annum would give the same return after 3 years?
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Answer
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Step 1:Convert annual interest rate to monthly rate
i = \frac{8.6\%}{12} = 0.7167\% = 0.007167
Divide the annual rate by 12 to get the monthly rate as a decimal.
Step 2:Calculate amount after 1 year (12 months)
A = 20000 \times (1 + 0.007167)^{12}
Use the compound interest formula with n = 12 months.
Step 3:Calculate interest credited after 1 year
\text{Interest} = A - 20000
Subtract the initial principal from the amount after 1 year.
Final Answer
\text{Interest} = 20000 \times (1 + 0.007167)^{12} - 20000 \approx 1786.94
The interest credited after the first year is approximately K^1786.94.
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