Question
2 Omphile wishes to have R10 000 in five years. He can invest R2 000 now. Determine the interest rate he will need to receive compounded annually. At what compound interest rate do I need to invest R12000 for my investment to grow to R 16500 in seven years? Palesa invests R2 000 in an account that offers her a \( 9.5 \% \) compound interest rate p.a. Alter two years she moves her money to an investment bank that can offer her an \( 11.2 \% \mathrm{growth} \). compounded annually, on her investment. How much is Palesa's investment worth after 8 years? Ethan invests R 10000 in a saving account, where interest is calculated at 8,75\% p.a. compounded annually. After two years he invests a further R 2000 in the account and three years after that he withdraws R 4500 . Determine how much money Ethan will have at the end of 8 years.
Ask by Guerrero Lindsey.
Mar 05,2025 17:34
UpStudy AI Solution
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Answer
- Omphile needs an interest rate of approximately **37.97%** compounded annually to reach R10,000 in 5 years.
- To grow R12,000 to R16,500 in 7 years, the required interest rate is approximately **4.87%** compounded annually.
- Palesa's investment will be worth approximately **R4,534.06** after 8 years.
- Ethan will have approximately **R8,038.94** at the end of 8 years.
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Beyond the Answer
To determine the interest rate Omphile needs, we use the formula for compound interest: \( A = P(1 + r)^n \). Plugging in his values (R10,000 for A, R2,000 for P, and 5 for n), we can rearrange it to find \( r \) when \( A = R10,000 \): \( r = (A/P)^{1/n} - 1 \). After calculating, Omphile would need an interest rate of approximately 28.79% compounded annually to achieve his goal.
For the second part regarding the compound interest growth for Palesa, she starts with R2,000 at a 9.5% rate for two years. After that, she moves her funds to an account with an 11.2% rate. By the end of year 2, her investment will grow to approximately R2,402. After moving, with the new rate applied over the next six years, she’ll end up with around R4,762.09, making her total investment worth about R4,762.09 after eight years.
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