Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
Correct Answer
$9630
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5350 ×10/100 × 8
= 5350 × 10 × 8/100
= 53500 × 8/100
= 428000/100
= $4280
Thus, Simple Interest = $4280
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 + $4280
= $9630
Thus, Amount to be paid = $9630 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 8)
= $5350 + ($5350 ×10/100 × 8)
= $5350 + (5350 × 10 × 8/100)
= $5350 + (53500 × 8/100)
= $5350 + (428000/100)
= $5350 + $4280 = $9630
Thus, Amount (A) to be paid = $9630 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $535 × 8 = $4280
Thus, Simple Interest (SI) = $4280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4280
= $9630
Thus, Amount to be paid = $9630 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(2) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(5) 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.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(7) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.