Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6077
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 9 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% × 9
= $5150 ×2/100 × 9
= 5150 × 2 × 9/100
= 10300 × 9/100
= 92700/100
= $927
Thus, Simple Interest = $927
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 + $927
= $6077
Thus, Amount to be paid = $6077 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) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 9)
= $5150 + ($5150 ×2/100 × 9)
= $5150 + (5150 × 2 × 9/100)
= $5150 + (10300 × 9/100)
= $5150 + (92700/100)
= $5150 + $927 = $6077
Thus, Amount (A) to be paid = $6077 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 9 years
= Simple interest for 1 year × 9
= $103 × 9 = $927
Thus, Simple Interest (SI) = $927
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $927
= $6077
Thus, Amount to be paid = $6077 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(5) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?