Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
Correct Answer
$7757.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5350 ×5/100 × 9
= 5350 × 5 × 9/100
= 26750 × 9/100
= 240750/100
= $2407.5
Thus, Simple Interest = $2407.5
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 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 5% × 9)
= $5350 + ($5350 ×5/100 × 9)
= $5350 + (5350 × 5 × 9/100)
= $5350 + (26750 × 9/100)
= $5350 + (240750/100)
= $5350 + $2407.5 = $7757.5
Thus, Amount (A) to be paid = $7757.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5350, the simple interest in 1 year
= 5/100 × 5350
= 5 × 5350/100
= 26750/100 = $267.5
Thus, simple interest for 1 year = $267.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $267.5 × 9 = $2407.5
Thus, Simple Interest (SI) = $2407.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 Answer
Similar Questions
(1) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(3) 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.
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.