Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
Correct Answer
$6327
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 2%
Time (t) = 7 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) = $5550 × 2% × 7
= $5550 ×2/100 × 7
= 5550 × 2 × 7/100
= 11100 × 7/100
= 77700/100
= $777
Thus, Simple Interest = $777
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 = $5550 + $777
= $6327
Thus, Amount to be paid = $6327 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 = $5550
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 2% × 7)
= $5550 + ($5550 ×2/100 × 7)
= $5550 + (5550 × 2 × 7/100)
= $5550 + (11100 × 7/100)
= $5550 + (77700/100)
= $5550 + $777 = $6327
Thus, Amount (A) to be paid = $6327 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 $5550, the simple interest in 1 year
= 2/100 × 5550
= 2 × 5550/100
= 11100/100 = $111
Thus, simple interest for 1 year = $111
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $111 × 7 = $777
Thus, Simple Interest (SI) = $777
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $777
= $6327
Thus, Amount to be paid = $6327 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(9) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.