Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
Correct Answer
$6572
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 3% × 8
= $5300 ×3/100 × 8
= 5300 × 3 × 8/100
= 15900 × 8/100
= 127200/100
= $1272
Thus, Simple Interest = $1272
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1272
= $6572
Thus, Amount to be paid = $6572 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 8)
= $5300 + ($5300 ×3/100 × 8)
= $5300 + (5300 × 3 × 8/100)
= $5300 + (15900 × 8/100)
= $5300 + (127200/100)
= $5300 + $1272 = $6572
Thus, Amount (A) to be paid = $6572 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $159 × 8 = $1272
Thus, Simple Interest (SI) = $1272
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1272
= $6572
Thus, Amount to be paid = $6572 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.