Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
Correct Answer
$4032
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 7%
Time (t) = 4 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) = $3150 × 7% × 4
= $3150 ×7/100 × 4
= 3150 × 7 × 4/100
= 22050 × 4/100
= 88200/100
= $882
Thus, Simple Interest = $882
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 = $3150 + $882
= $4032
Thus, Amount to be paid = $4032 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 = $3150
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 7% × 4)
= $3150 + ($3150 ×7/100 × 4)
= $3150 + (3150 × 7 × 4/100)
= $3150 + (22050 × 4/100)
= $3150 + (88200/100)
= $3150 + $882 = $4032
Thus, Amount (A) to be paid = $4032 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 $3150, the simple interest in 1 year
= 7/100 × 3150
= 7 × 3150/100
= 22050/100 = $220.5
Thus, simple interest for 1 year = $220.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $220.5 × 4 = $882
Thus, Simple Interest (SI) = $882
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $882
= $4032
Thus, Amount to be paid = $4032 Answer
Similar Questions
(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(2) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(3) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(6) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(8) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.