Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
Correct Answer
$4260
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3550 × 5% × 4
= $3550 ×5/100 × 4
= 3550 × 5 × 4/100
= 17750 × 4/100
= 71000/100
= $710
Thus, Simple Interest = $710
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 = $3550 + $710
= $4260
Thus, Amount to be paid = $4260 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 = $3550
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 4)
= $3550 + ($3550 ×5/100 × 4)
= $3550 + (3550 × 5 × 4/100)
= $3550 + (17750 × 4/100)
= $3550 + (71000/100)
= $3550 + $710 = $4260
Thus, Amount (A) to be paid = $4260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3550, the simple interest in 1 year
= 5/100 × 3550
= 5 × 3550/100
= 17750/100 = $177.5
Thus, simple interest for 1 year = $177.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $177.5 × 4 = $710
Thus, Simple Interest (SI) = $710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $710
= $4260
Thus, Amount to be paid = $4260 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(4) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?