Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6180
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5150 ×2/100 × 10
= 5150 × 2 × 10/100
= 10300 × 10/100
= 103000/100
= $1030
Thus, Simple Interest = $1030
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 + $1030
= $6180
Thus, Amount to be paid = $6180 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 10)
= $5150 + ($5150 ×2/100 × 10)
= $5150 + (5150 × 2 × 10/100)
= $5150 + (10300 × 10/100)
= $5150 + (103000/100)
= $5150 + $1030 = $6180
Thus, Amount (A) to be paid = $6180 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $103 × 10 = $1030
Thus, Simple Interest (SI) = $1030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1030
= $6180
Thus, Amount to be paid = $6180 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(5) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(10) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?