Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6180
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5150 ×2/100 × 10
= 5150 × 2 × 10/100
= 10300 × 10/100
= 103000/100
= $1030
Thus, Simple Interest = $1030
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 + $1030
= $6180
Thus, Amount to be paid = $6180 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 10)
= $5150 + ($5150 ×2/100 × 10)
= $5150 + (5150 × 2 × 10/100)
= $5150 + (10300 × 10/100)
= $5150 + (103000/100)
= $5150 + $1030 = $6180
Thus, Amount (A) to be paid = $6180 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $103 × 10 = $1030
Thus, Simple Interest (SI) = $1030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1030
= $6180
Thus, Amount to be paid = $6180 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(3) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.