Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
Correct Answer
$8346
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5350 ×8/100 × 7
= 5350 × 8 × 7/100
= 42800 × 7/100
= 299600/100
= $2996
Thus, Simple Interest = $2996
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 + $2996
= $8346
Thus, Amount to be paid = $8346 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5350 + ($5350 × 8% × 7)
= $5350 + ($5350 ×8/100 × 7)
= $5350 + (5350 × 8 × 7/100)
= $5350 + (42800 × 7/100)
= $5350 + (299600/100)
= $5350 + $2996 = $8346
Thus, Amount (A) to be paid = $8346 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5350, the simple interest in 1 year
= 8/100 × 5350
= 8 × 5350/100
= 42800/100 = $428
Thus, simple interest for 1 year = $428
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $428 × 7 = $2996
Thus, Simple Interest (SI) = $2996
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2996
= $8346
Thus, Amount to be paid = $8346 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(7) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?