Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
Correct Answer
$9785
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 9% × 10
= $5150 ×9/100 × 10
= 5150 × 9 × 10/100
= 46350 × 10/100
= 463500/100
= $4635
Thus, Simple Interest = $4635
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 = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 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 = $5150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 10)
= $5150 + ($5150 ×9/100 × 10)
= $5150 + (5150 × 9 × 10/100)
= $5150 + (46350 × 10/100)
= $5150 + (463500/100)
= $5150 + $4635 = $9785
Thus, Amount (A) to be paid = $9785 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 $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $463.5 × 10 = $4635
Thus, Simple Interest (SI) = $4635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(7) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(9) 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.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.