Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
Correct Answer
$7918
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5350 ×6/100 × 8
= 5350 × 6 × 8/100
= 32100 × 8/100
= 256800/100
= $2568
Thus, Simple Interest = $2568
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 + $2568
= $7918
Thus, Amount to be paid = $7918 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 6% × 8)
= $5350 + ($5350 ×6/100 × 8)
= $5350 + (5350 × 6 × 8/100)
= $5350 + (32100 × 8/100)
= $5350 + (256800/100)
= $5350 + $2568 = $7918
Thus, Amount (A) to be paid = $7918 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5350, the simple interest in 1 year
= 6/100 × 5350
= 6 × 5350/100
= 32100/100 = $321
Thus, simple interest for 1 year = $321
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $321 × 8 = $2568
Thus, Simple Interest (SI) = $2568
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2568
= $7918
Thus, Amount to be paid = $7918 Answer
Similar Questions
(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(7) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(8) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(10) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.