maria borrowed Rs 1400 at the rate of 6%(p.a) for 8 yers and 5 months .Find the amount she paid back?
1400,6%8year 5month
To find the amount Maria paid back, we need to calculate the total amount, including interest, that she paid over the 8 years and 5 months.
Step 1: Convert 5 months into years. We divide 5 months by 12 months (as there are 12 months in a year).
5 months ÷ 12 months/year = 0.42 years (rounded to two decimal places)
Step 2: Add the 8 years and 0.42 years together.
8 years + 0.42 years = 8.42 years
Step 3: Calculate the total amount using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount (including interest)
P = Principal amount (initial borrowed amount)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = Rs 1400
r = 6% (or 0.06 as a decimal)
n = 1 (as the interest is compounded annually)
t = 8.42 years
A = 1400(1 + 0.06/1)^(1 * 8.42)
Step 4: Calculate the total amount.
A = 1400(1 + 0.06)^(8.42)
A = 1400(1.06^8.42)
A ≈ 1400 * 1.490
A ≈ Rs 2086
Therefore, Maria paid back approximately Rs 2086.
To find the amount Maria paid back, we need to calculate the total amount paid, which includes the principal amount borrowed plus the interest.
First, let's calculate the interest.
The formula to calculate simple interest is:
Interest = (Principal * Rate * Time) / 100
Given:
Principal amount (P) = Rs 1400
Rate (R) = 6% per annum
Time (T) = 8 years and 5 months
Converting the time to years, we have:
Time = 8 + (5/12) years
Now we can substitute these values into the formula to calculate the interest:
Interest = (1400 * 6 * (8 + (5/12))) / 100
Calculating this expression gives us the interest amount.
Once we have the interest, we can find the total amount paid back by adding the interest to the principal amount:
Total Amount = Principal + Interest
Calculating this expression will give us the final answer, which is the amount Maria paid back.
1400(1+(8 5/12)*.06) = 2107
makes sense, since 8 1/3 * 6% = 50%