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?

Answer 1

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.

Answer 2

5. What sum of money will amount to Birr 21296 in 3 years at 10% per annum, compounded annually?

Answer 3

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.

Answer 4

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

Answer 5

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.