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) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.