Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
Correct Answer
$6206
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5350 ×2/100 × 8
= 5350 × 2 × 8/100
= 10700 × 8/100
= 85600/100
= $856
Thus, Simple Interest = $856
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 + $856
= $6206
Thus, Amount to be paid = $6206 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 2% × 8)
= $5350 + ($5350 ×2/100 × 8)
= $5350 + (5350 × 2 × 8/100)
= $5350 + (10700 × 8/100)
= $5350 + (85600/100)
= $5350 + $856 = $6206
Thus, Amount (A) to be paid = $6206 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5350, the simple interest in 1 year
= 2/100 × 5350
= 2 × 5350/100
= 10700/100 = $107
Thus, simple interest for 1 year = $107
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $107 × 8 = $856
Thus, Simple Interest (SI) = $856
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $856
= $6206
Thus, Amount to be paid = $6206 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.