Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
Correct Answer
$7276
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5350 ×4/100 × 9
= 5350 × 4 × 9/100
= 21400 × 9/100
= 192600/100
= $1926
Thus, Simple Interest = $1926
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 + $1926
= $7276
Thus, Amount to be paid = $7276 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 4% × 9)
= $5350 + ($5350 ×4/100 × 9)
= $5350 + (5350 × 4 × 9/100)
= $5350 + (21400 × 9/100)
= $5350 + (192600/100)
= $5350 + $1926 = $7276
Thus, Amount (A) to be paid = $7276 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5350, the simple interest in 1 year
= 4/100 × 5350
= 4 × 5350/100
= 21400/100 = $214
Thus, simple interest for 1 year = $214
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $214 × 9 = $1926
Thus, Simple Interest (SI) = $1926
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $1926
= $7276
Thus, Amount to be paid = $7276 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(9) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.