Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
Correct Answer
$4295.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 7%
Time (t) = 3 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) = $3550 × 7% × 3
= $3550 ×7/100 × 3
= 3550 × 7 × 3/100
= 24850 × 3/100
= 74550/100
= $745.5
Thus, Simple Interest = $745.5
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 = $3550 + $745.5
= $4295.5
Thus, Amount to be paid = $4295.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 7% × 3)
= $3550 + ($3550 ×7/100 × 3)
= $3550 + (3550 × 7 × 3/100)
= $3550 + (24850 × 3/100)
= $3550 + (74550/100)
= $3550 + $745.5 = $4295.5
Thus, Amount (A) to be paid = $4295.5 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 $3550, the simple interest in 1 year
= 7/100 × 3550
= 7 × 3550/100
= 24850/100 = $248.5
Thus, simple interest for 1 year = $248.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $248.5 × 3 = $745.5
Thus, Simple Interest (SI) = $745.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $745.5
= $4295.5
Thus, Amount to be paid = $4295.5 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(5) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(7) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(9) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?