sarushrestha1858
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2. You have to deposit Rs 50,000 in a bank for 2 years. The table below provides information on the rate of interest of two banks.

| Bank | Interest Rate |
|------|---------------|
| A | Yearly compound interest = 6% |
| B | Half-yearly compound interest = 5% |

a) Calculate the interest earned by saving the money in Bank A and Bank B.
b) In which bank would you save money and why? Provide reasons.

Sagot :

GinnyAnswer
Alright, let's tackle the question step-by-step.

### Part (a): Calculating Interest

#### For Bank A:
Bank A offers a yearly compound interest rate of 6%.

The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Here:
- [tex]\( P \)[/tex] is the principal amount = Rs. 50,000
- [tex]\( r \)[/tex] is the annual interest rate = 6% = 0.06
- [tex]\( t \)[/tex] is the time the money is invested for = 2 years
- [tex]\( n \)[/tex] is the number of times interest applied per time period, indicating 1 for yearly compounding.

So, substituting the values given:
[tex]\[ A_A = 50000 \left(1 + 0.06\right)^2 \][/tex]
[tex]\[ A_A = 50000 \left(1.06\right)^2 \][/tex]
[tex]\[ A_A = 50000 \times 1.1236 \approx 56180 \][/tex]

The interest earned can be calculated as:
[tex]\[ \text{Interest}_A = A_A - P \][/tex]
[tex]\[ \text{Interest}_A = 56180 - 50000 \][/tex]
[tex]\[ \text{Interest}_A = 6180.00 \][/tex]

#### For Bank B:
Bank B offers a half-yearly compound interest rate of 5%.

The formula for compound interest in this case remains the same, but we need to adjust [tex]\( n \)[/tex] to reflect half-yearly compounding.

Here:
- [tex]\( P \)[/tex] is the principal amount = Rs. 50,000
- [tex]\( r \)[/tex] is the annual interest rate = 5% = 0.05
- [tex]\( t \)[/tex] is the time the money is invested for = 2 years
- [tex]\( n \)[/tex] is the number of times interest applied per time period = 2 (since it's half-yearly).

So, substituting the values given:
[tex]\[ A_B = 50000 \left(1 + \frac{0.05}{2}\right)^{2 \times 2} \][/tex]
[tex]\[ A_B = 50000 \left(1 + 0.025\right)^4 \][/tex]
[tex]\[ A_B = 50000 \left(1.025\right)^4 \][/tex]
[tex]\[ A_B = 50000 \times 1.2155 \approx 55190.64 \][/tex]

The interest earned can be calculated as:
[tex]\[ \text{Interest}_B = A_B - P \][/tex]
[tex]\[ \text{Interest}_B = 55190.64 - 50000 \][/tex]
[tex]\[ \text{Interest}_B = 5190.64 \][/tex]

### Part (b): Which Bank to Save Money In and Why?

Now we need to compare the interests earned from both banks:

- Interest from Bank A: Rs 6180.00
- Interest from Bank B: Rs 5190.64

Clearly, the interest earned from Bank A is higher than that from Bank B.

Conclusion:
You should save your money in Bank A because, after 2 years, it will yield an interest of Rs 6180.00, which is higher than the interest earned from Bank B, which is Rs 5190.64. Therefore, choosing Bank A will provide you with better returns on your investment.
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