Tim buys unit trusts for R25 000 after eight years he sells them R63 000 (a)calculate a compound interest rate that would yield the same return (b)calculate a simple interest rate that would provide the same growth
To calculate the compound interest rate that would yield the same return, we can use the compound interest formula:
Future Value = Principal * (1 + Interest Rate)^Time
In this case, Principal = R25,000, Future Value = R63,000, and Time = 8 years.
1. Rearrange the formula to solve for the interest rate:
(1 + Interest Rate) = Future Value / Principal
2. Substitute the given values:
(1 + Interest Rate) = R63,000 / R25,000
3. Calculate the interest rate:
Interest Rate = (R63,000 / R25,000) - 1
Interest Rate = 2.52 - 1
Interest Rate = 1.52
Therefore, the compound interest rate that would yield the same return is 152%.
To calculate the simple interest rate that would provide the same growth, we can use the simple interest formula:
Future Value = Principal + (Principal * Interest Rate * Time)
In this case, Principal = R25,000, Future Value = R63,000, and Time = 8 years.
1. Rearrange the formula to solve for the interest rate:
Interest Rate = (Future Value - Principal) / (Principal * Time)
2. Substitute the given values:
Interest Rate = (R63,000 - R25,000) / (R25,000 * 8)
3. Calculate the interest rate:
Interest Rate = R38,000 / R200,000
Interest Rate = 0.19
Therefore, the simple interest rate that would provide the same growth is 19%.