Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
Correct Answer
$6634
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5350 × 3% × 8
= $5350 ×3/100 × 8
= 5350 × 3 × 8/100
= 16050 × 8/100
= 128400/100
= $1284
Thus, Simple Interest = $1284
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 = $5350 + $1284
= $6634
Thus, Amount to be paid = $6634 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 = $5350
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 3% × 8)
= $5350 + ($5350 ×3/100 × 8)
= $5350 + (5350 × 3 × 8/100)
= $5350 + (16050 × 8/100)
= $5350 + (128400/100)
= $5350 + $1284 = $6634
Thus, Amount (A) to be paid = $6634 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5350, the simple interest in 1 year
= 3/100 × 5350
= 3 × 5350/100
= 16050/100 = $160.5
Thus, simple interest for 1 year = $160.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $160.5 × 8 = $1284
Thus, Simple Interest (SI) = $1284
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $1284
= $6634
Thus, Amount to be paid = $6634 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(4) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(10) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.