4. Robel obtained a loan of Birr 250,000 from the commercial bank of Ethiopia. If the rate of interest is 8% per annum compounded annually and repaid Birr 50, 000 at the end of first year. What amount will he has to pay to the bank after 2 years to discharge his debt?
To solve this problem, we need to calculate the remaining balance after the first year and then add the interest for the second year.
After the first year, Robel repaid Birr 50,000. Therefore, the remaining balance is:
250,000 - 50,000 = Birr 200,000
Now, we need to calculate the interest for the second year. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (initial loan amount)
r = annual interest rate (8% or 0.08)
n = number of times interest is compounded per year (compounded annually, so n = 1)
t = number of years (2)
Plugging in the values:
A = 200,000(1 + 0.08/1)^(1*2)
= 200,000(1 + 0.08)^2
= 200,000(1.08)^2
= 200,000(1.1664)
= Birr 233,280
Therefore, Robel will have to pay Birr 233,280 to the bank after 2 years to discharge his debt.
5. What sum of money will amount to Birr 21296 in 3 years at 10% per annum, compounded annually?
To find the principal amount that will amount to Birr 21,296 in 3 years at a 10% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount
r = annual interest rate
n = number of times interest is compounded per year
t = number of years
Given:
A = Birr 21,296
r = 10% or 0.10
n = 1 (compounded annually)
t = 3
Plugging in the values:
21,296 = P(1 + 0.10/1)^(1*3)
Dividing both sides by (1.10)^3:
21,296 / (1.10)^3 = P
Calculating (1.10)^3:
21,296 / 1.331 = P
P ≈ Birr 15,999.40
Therefore, a principal amount of approximately Birr 15,999.40 will amount to Birr 21,296 in 3 years at a 10% interest rate compounded annually.
2. Compare the simple interest and compound interest on Birr 8,000 at 10 % per annum for three years if the interest is compounded annually
To compare the simple interest and compound interest on Birr 8,000 at a 10% interest rate per annum for three years, we can calculate both using the formulas for simple interest and compound interest.
Simple Interest:
Simple interest is calculated using the formula:
I = P * r * t
Where:
I = interest
P = principal amount
r = annual interest rate
t = number of years
For the given values:
P = Birr 8,000
r = 10% or 0.10
t = 3
Substituting the values into the formula:
I = 8,000 * 0.10 * 3
= Birr 2,400
Therefore, the simple interest after three years would be Birr 2,400.
Compound Interest:
Compound interest is calculated using the formula:
A = P * (1 + r/n)^(nt) - P
Where:
A = amount (including principal and interest)
P = principal amount
r = annual interest rate
n = number of times interest is compounded per year
t = number of years
For the given values:
P = Birr 8,000
r = 10% or 0.10
n = 1 (compounded annually)
t = 3
Substituting the values into the formula:
A = 8,000 * (1 + 0.10/1)^(1*3) - 8,000
≈ 8,000 * (1.10)^3 - 8,000
≈ 8,000 * 1.331 - 8,000
≈ Birr 10,648 - 8,000
≈ Birr 2,648
Therefore, the compound interest after three years would be Birr 2,648.
In conclusion, the simple interest would be Birr 2,400 and the compound interest would be Birr 2,648 for Birr 8,000 at a 10% interest rate compounded annually for three years.
To find the total amount that Robel will have to pay to the bank after 2 years, we need to calculate the amount remaining on the loan after the first year and then add the interest for the second year.
Step 1: Calculate the remaining loan amount after the first year.
The loan amount is Birr 250,000.
Robel repaid Birr 50,000 at the end of the first year.
Therefore, the remaining loan amount after the first year is:
250,000 - 50,000 = Birr 200,000.
Step 2: Calculate the interest for the second year.
The interest rate is 8% per annum compounded annually.
To calculate compound interest, we use the formula:
Compound Interest = Principal Amount * (1 + (Interest Rate/100))^Time - Principal Amount
where Principal Amount is the remaining loan amount after the first year, Interest Rate is 8%, and Time is 1 year.
Substituting the values into the formula, we get:
Interest = 200,000 * (1 + (8/100))^1 - 200,000
= 200,000 * (1 + 0.08) - 200,000
= 200,000 * 1.08 - 200,000
= 216,000 - 200,000
= Birr 16,000.
Step 3: Add the remaining loan amount and the interest for the second year.
The remaining loan amount after the first year is Birr 200,000.
The interest for the second year is Birr 16,000.
Therefore, Robel will have to pay a total of:
200,000 + 16,000 = Birr 216,000 to the bank after 2 years to discharge his debt.
To calculate the amount that Robel will have to pay to the bank after 2 years to discharge his debt, we need to understand compound interest. Compound interest is when the interest on a loan or investment is calculated not only on the initial principal amount but also on any previously accrued interest.
Let's break down the problem step by step:
1. Start with the initial loan amount: Robel obtained a loan of Birr 250,000.
2. Note the interest rate: The rate of interest is 8% per annum compounded annually. This means that the interest is added to the loan amount once every year.
3. Calculate the interest for the first year: Robel repaid Birr 50,000 at the end of the first year. So, the remaining loan amount after one year will be Birr 250,000 - Birr 50,000 = Birr 200,000.
To calculate the interest for the first year, we use the formula:
Interest = Principal × Rate
= Birr 200,000 × 8% = Birr 16,000.
4. Calculate the remaining loan amount after the first year: The remaining loan amount after the first year, including the interest, will be Birr 200,000 + Birr 16,000 = Birr 216,000.
5. Calculate the interest for the second year: Since the interest is compounded annually, we need to calculate the interest on the remaining loan amount after the first year.
Interest for the second year = Remaining loan amount after the first year × Rate
= Birr 216,000 × 8% = Birr 17,280.
6. Calculate the total loan amount after 2 years: The total loan amount after 2 years will be the remaining loan amount after the first year plus the interest for the second year.
Total loan amount after 2 years = Remaining loan amount after the first year + Interest for the second year
= Birr 216,000 + Birr 17,280 = Birr 233,280.
Therefore, Robel will have to pay Birr 233,280 to the bank after 2 years to discharge his debt.