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) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(4) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(6) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(10) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.