Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
Correct Answer
$5871
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 7 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% × 7
= $5150 ×2/100 × 7
= 5150 × 2 × 7/100
= 10300 × 7/100
= 72100/100
= $721
Thus, Simple Interest = $721
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 + $721
= $5871
Thus, Amount to be paid = $5871 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) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 7)
= $5150 + ($5150 ×2/100 × 7)
= $5150 + (5150 × 2 × 7/100)
= $5150 + (10300 × 7/100)
= $5150 + (72100/100)
= $5150 + $721 = $5871
Thus, Amount (A) to be paid = $5871 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 7 years
= Simple interest for 1 year × 7
= $103 × 7 = $721
Thus, Simple Interest (SI) = $721
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $721
= $5871
Thus, Amount to be paid = $5871 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?