Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
Correct Answer
$6592
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5150 ×4/100 × 7
= 5150 × 4 × 7/100
= 20600 × 7/100
= 144200/100
= $1442
Thus, Simple Interest = $1442
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 + $1442
= $6592
Thus, Amount to be paid = $6592 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 7)
= $5150 + ($5150 ×4/100 × 7)
= $5150 + (5150 × 4 × 7/100)
= $5150 + (20600 × 7/100)
= $5150 + (144200/100)
= $5150 + $1442 = $6592
Thus, Amount (A) to be paid = $6592 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $206 × 7 = $1442
Thus, Simple Interest (SI) = $1442
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1442
= $6592
Thus, Amount to be paid = $6592 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(2) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.
(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?