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) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(7) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.