Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
Correct Answer
$10165
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5350 ×9/100 × 10
= 5350 × 9 × 10/100
= 48150 × 10/100
= 481500/100
= $4815
Thus, Simple Interest = $4815
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 + $4815
= $10165
Thus, Amount to be paid = $10165 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 9% × 10)
= $5350 + ($5350 ×9/100 × 10)
= $5350 + (5350 × 9 × 10/100)
= $5350 + (48150 × 10/100)
= $5350 + (481500/100)
= $5350 + $4815 = $10165
Thus, Amount (A) to be paid = $10165 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5350, the simple interest in 1 year
= 9/100 × 5350
= 9 × 5350/100
= 48150/100 = $481.5
Thus, simple interest for 1 year = $481.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $481.5 × 10 = $4815
Thus, Simple Interest (SI) = $4815
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4815
= $10165
Thus, Amount to be paid = $10165 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(3) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.