sofia deposits birr 3500 in a bank account paying an annual interest rate of 6%. find the amount she has at the end of the fourth year?
What if the amount she has at the end of the second year
well, she earns 6% each year, so each year she multiplies the 3500 by 1.06, right?
so, after 4 years, she has 3500 * 1.06^4 = ?
To find the amount Sofia has at the end of the fourth year, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = 3500 birr
r = 6% = 0.06
n = 1 (compounded annually)
t = 4 years
Substituting the values into the formula:
A = 3500(1 + 0.06/1)^(1×4)
A = 3500(1 + 0.06)^4
A = 3500(1.06)^4
Calculating:
A ≈ 3500 × 1.262476
A ≈ 4423.67 birr
Therefore, Sofia has approximately 4423.67 birr at the end of the fourth year.
To find the amount Sofia has at the end of the fourth year, we need to calculate the compound interest.
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Sofia deposited Birr 3500, the annual interest rate is 6%, and we want to calculate the amount at the end of the fourth year.
Plugging in the values into the formula:
P = 3500
r = 0.06 (6% expressed as a decimal)
n = 1 (interest compounded annually)
t = 4
A = 3500(1 + 0.06/1)^(1*4)
A = 3500(1 + 0.06)^4
Now, let's calculate the final amount using a calculator:
A = 3500(1.06)^4
A ≈ 3500(1.26248)
A ≈ 4428.68
Therefore, Sofia will have approximately Birr 4428.68 at the end of the fourth year.