Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
Correct Answer
$8034
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5150 ×7/100 × 8
= 5150 × 7 × 8/100
= 36050 × 8/100
= 288400/100
= $2884
Thus, Simple Interest = $2884
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 + $2884
= $8034
Thus, Amount to be paid = $8034 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) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 8)
= $5150 + ($5150 ×7/100 × 8)
= $5150 + (5150 × 7 × 8/100)
= $5150 + (36050 × 8/100)
= $5150 + (288400/100)
= $5150 + $2884 = $8034
Thus, Amount (A) to be paid = $8034 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 8 years
= Simple interest for 1 year × 8
= $360.5 × 8 = $2884
Thus, Simple Interest (SI) = $2884
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2884
= $8034
Thus, Amount to be paid = $8034 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(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) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.