Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
Correct Answer
$6695
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5150 × 3% × 10
= $5150 ×3/100 × 10
= 5150 × 3 × 10/100
= 15450 × 10/100
= 154500/100
= $1545
Thus, Simple Interest = $1545
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 = $5150 + $1545
= $6695
Thus, Amount to be paid = $6695 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 = $5150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 10)
= $5150 + ($5150 ×3/100 × 10)
= $5150 + (5150 × 3 × 10/100)
= $5150 + (15450 × 10/100)
= $5150 + (154500/100)
= $5150 + $1545 = $6695
Thus, Amount (A) to be paid = $6695 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 $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $154.5 × 10 = $1545
Thus, Simple Interest (SI) = $1545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1545
= $6695
Thus, Amount to be paid = $6695 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(2) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.