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Questions and Answers
What is the total interest earned on the initial investment after 8 years at a rate of 15% per annum?
What is the total interest earned on the initial investment after 8 years at a rate of 15% per annum?
- Rs.1,200 (correct)
- Rs.1,500
- Rs.900
- Rs.600
If the amount received after reinvestment was Rs.1,536 more than the initial investment, what was this total amount after reinvestment?
If the amount received after reinvestment was Rs.1,536 more than the initial investment, what was this total amount after reinvestment?
- Rs.2,036
- Rs.2,536 (correct)
- Rs.2,136
- Rs.2,436
What is the formula for calculating the total amount after reinvesting an amount at an interest rate?
What is the formula for calculating the total amount after reinvesting an amount at an interest rate?
- Total Amount = Principal + Rate + Time
- Total Amount = Principal + (Rate × Time)
- Total Amount = Principal × (1 + Rate)^Time (correct)
- Total Amount = Principal² × Rate × Time
If Rs.1,536 is the difference between the total received after reinvestment and the initial investment, which of the following values for Rs. X would be valid?
If Rs.1,536 is the difference between the total received after reinvestment and the initial investment, which of the following values for Rs. X would be valid?
What is the effective annual growth rate of the investment after reinvesting for another 8 years at 15% per annum?
What is the effective annual growth rate of the investment after reinvesting for another 8 years at 15% per annum?
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Study Notes
Investment Details
- An initial sum of money (Rs. X) was invested.
- The investment earned interest at a 15% annual rate.
- The investment period was 8 years.
- After 8 years, the accumulated amount was reinvested under the same conditions (15% interest, 8 years).
- The final amount after the second investment period was Rs. 1,536 more than the initial investment (Rs. X).
Compound Interest Calculation
- The problem involves compound interest, where interest earned is added to the principal for subsequent interest calculations.
- The calculation needs to determine the initial principal (Rs. X) based on the final amount and the given interest rate and time periods.
- To solve, one needs to apply compound interest formula twice: once for the first 8-year period and again for the second 8-year period, equating the final amount to (X + 1536).
Possible Solution Approach
- A trial-and-error approach using the given multiple-choice answers could be used to find the value of X that satisfies the conditions.
- Alternatively, a more formal approach is to set up an equation using the compound interest formula and solve for X. This would involve using the formula A = P (1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year (assumed to be 1 in this case), and t is the time in years.
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