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The Partners A & B together lent Rs. 3903 at 4% p.a interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9 years. The share of A in the sum of Rs.3903/- would have beena)Rs.1875b)Rs.2280c)Rs.2028d)Rs.2820Correct answer is option 'C'. Can you explain this answer?
Ref: https://edurev.in/question/495383/The-Partners-A-B-together-lent-Rs-3903-at-4-p-a-interest-compounded-annually-After-a-span-of-7-ye
The compound interest formula:
Let the principal by A be x.Then that by B would be (3903−x).Here n=1, as the interest is compounded annually.The rate of interest,
The amount received by A after t=7 years,
Similarly, the amount received by B after 9 years,
It is stated that the amounts are equal. Then,x⋅(1.04)7=(3903−x)(1.04)9
Share of A in the original investment=Rs. 2028.
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FAQs on The compound interest formula & Solution - CA Foundation
| 1. What is the compound interest formula? |  |
Ans. The compound interest formula is a mathematical formula used to calculate the amount of interest earned or accrued on an initial amount of money, called the principal, over a specific period of time. The formula is: 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, and t is the number of years.
| 2. How is compound interest different from simple interest? | |
Ans. Compound interest is different from simple interest because it takes into account the interest earned on both the initial principal and any accumulated interest. In contrast, simple interest only calculates interest based on the principal amount. Compound interest generally results in higher returns or higher interest charges compared to simple interest over the same period of time.
| 3. How can the compound interest formula be used in real-life situations? | |
Ans. The compound interest formula can be used in various real-life situations, such as calculating the growth of investments, determining the cost of loans or credit card debts, and understanding the impact of compounding on savings accounts. By using the formula, individuals can make informed decisions about their finances and plan for their future financial goals.
| 4. What is the significance of the variables in the compound interest formula? | |
Ans. The variables in the compound interest formula have specific meanings. The principal (P) represents the initial amount of money, the interest rate (r) represents the annual interest rate, the number of times interest is compounded per year (n) represents the frequency of compounding, and the number of years (t) represents the time period for which interest is calculated. Understanding the significance of these variables helps in accurately calculating compound interest.
| 5. How does compounding frequency affect compound interest? | |
Ans. The compounding frequency, represented by the variable "n" in the compound interest formula, determines how often interest is compounded within a year. The more frequently interest is compounded, the greater the impact on the final amount. For example, if interest is compounded annually, the interest is added once a year. However, if interest is compounded quarterly, it is added four times a year, resulting in a higher total interest earned or charged over time. Therefore, a higher compounding frequency leads to higher compound interest.
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