Question:
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is [This Question was asked as TITA]
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is [This Question was asked as TITA]
Updated On: Jul 24, 2025
- 15000
- 17000
- 16000
- 18000
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
We are given:
- Final Amount \( A = 18522 \)
- Rate of Interest \( r = 10\% = 0.10 \)
- Time \( t = 1.5 \) years
- Compounded Half-Yearly → \( n = 2 \)
- Principal \( P = ? \)
The compound interest formula for half-yearly compounding is:
\[ A = P \left(1 + \frac{r}{n} \right)^{nt} \]
Substituting values:
\[ 18522 = P \left(1 + \frac{0.10}{2} \right)^{2 \times 1.5} \] \[ 18522 = P (1.05)^3 \] \[ 18522 = P \times 1.157625 \]
Solving for \( P \):
\[ P = \frac{18522}{1.157625} \approx 16000 \]
Final Answer: The initial principal invested was: \[ \boxed{16000} \]
Was this answer helpful?
0
0
Top Questions on SI & CI
- A sum of money triples itself in 8 years at simple interest. In how many years will it become five times itself at the same rate?
- Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
- S invested 22,000 for 6 years at a 4% rate compounded half-yearly. B also invested a certain amount of money for 5 years in the same scheme and then reinvested it for a year at a 10% rate of simple interest. If their total amounts become the same after 6 years, what was B’s initial investment?
- An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
- Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually.If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is
View More Questions
Questions Asked in CAT exam
- A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
- CAT - 2024
- Algebra
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- If m and n are natural numbers such that n > 1, and mn = 225 × 340, then m − n equals
- CAT - 2024
- Exponents and Powers
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
- \( 10^{68} \) is divided by 13, the remainder is is
- CAT - 2024
- Divisibility and Remainder
View More Questions