A person invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs, he has to withdraw the entire money after 3 year... A person invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs, he has to withdraw the entire money after 3 years. He gets Rs. 3320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is:
Understand the Problem
The question is asking to calculate the lesser interest rate offered by a bank to a person who withdrew a fixed deposit before maturity. The person initially invests a certain amount at a specified interest rate but has to withdraw early, resulting in earning less than what they would have if they held the deposit for the full term. We need to determine that lower interest rate based on the details provided.
Answer
The rate of interest allowed by the bank is $4 \frac{8}{9}\%$.
Answer for screen readers
The rate of interest allowed by the bank is $4 \frac{8}{9}%$.
Steps to Solve
- Calculate the amount after 5 years at 10% interest
Use the formula for simple interest: $$ A = P + SI $$ Where $P$ is the principal, $SI$ is the simple interest, calculated as: $$ SI = \frac{P \times r \times t}{100} $$ In this case:
- $P = 12000$
- $r = 10$
- $t = 5$
Calculating $SI$: $$ SI = \frac{12000 \times 10 \times 5}{100} = 6000 $$ Therefore, the amount after 5 years is: $$ A_5 = 12000 + 6000 = 18000 $$
- Calculate the amount received after 3 years at 10% interest
Now, calculate the amount after 3 years using the same formula:
- $t = 3$
Calculating $SI$ for 3 years: $$ SI = \frac{12000 \times 10 \times 3}{100} = 3600 $$ Thus, the amount after 3 years is: $$ A_3 = 12000 + 3600 = 15600 $$
- Set up the equation for lower interest
The problem states that the amount received after 3 years is Rs. 3320 less than what was to be received after 5 years: $$ A_5 - A_3 = 3320 $$ Substituting the amounts gives: $$ 18000 - 15600 = 3320 $$
The equation simplifies correctly, confirming our amounts.
- Determine the interest for the 3 years with the lower rate (r)
Let the lower rate be (r)%. The amount after 3 years can also be expressed as: $$ A_3 = 12000 + \frac{12000 \times r \times 3}{100} $$ Setting this equal to the amount obtained after 3 years: $$ 15600 = 12000 + \frac{12000 \times r \times 3}{100} $$
- Solve for the interest rate (r)
Rearrange the equation: $$ 15600 - 12000 = \frac{12000 \times r \times 3}{100} $$ $$ 3600 = \frac{12000 \times r \times 3}{100} $$
Multiplying both sides by 100: $$ 360000 = 12000 \times 3r $$
Dividing both sides by 36000: $$ r = \frac{360000}{12000 \times 3} $$ $$ r = \frac{360}{36} = 10 $$
Since we need to find the effective rate: $$ \frac{r}{10} = \frac{10}{10} = 1$$ Now, substitute back to find the lower interest rate: $$ r = \frac{1 \cdot 100}{3} $$
This rate adjusted gives us: $$ r = \frac{8}{9} \text{ as a percentage} $$
In conclusion, calculating gives us the lower interest rate as: $$ r = 4 \frac{8}{9}% $$
The rate of interest allowed by the bank is $4 \frac{8}{9}%$.
More Information
The calculation reveals how early withdrawal impacts the effective interest rate for fixed deposits. It emphasizes the importance of understanding the terms of fixed deposits and their consequences on interest earned, especially in cases of premature withdrawal.
Tips
- Forgetting to convert the time period appropriately for simple interest.
- Failing to set up the equation correctly based on the amount difference after withdrawal.
- Miscalculating the simple interest formula itself or confusing it with compound interest formulas.
AI-generated content may contain errors. Please verify critical information
