Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
Correct Answer
$7673.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7
= $5150 ×7/100 × 7
= 5150 × 7 × 7/100
= 36050 × 7/100
= 252350/100
= $2523.5
Thus, Simple Interest = $2523.5
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 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 7)
= $5150 + ($5150 ×7/100 × 7)
= $5150 + (5150 × 7 × 7/100)
= $5150 + (36050 × 7/100)
= $5150 + (252350/100)
= $5150 + $2523.5 = $7673.5
Thus, Amount (A) to be paid = $7673.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $360.5 × 7 = $2523.5
Thus, Simple Interest (SI) = $2523.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.