Question:
Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
Correct Answer
$8195
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5500 × 7% × 7
= $5500 ×7/100 × 7
= 5500 × 7 × 7/100
= 38500 × 7/100
= 269500/100
= $2695
Thus, Simple Interest = $2695
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 = $5500 + $2695
= $8195
Thus, Amount to be paid = $8195 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 = $5500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 7)
= $5500 + ($5500 ×7/100 × 7)
= $5500 + (5500 × 7 × 7/100)
= $5500 + (38500 × 7/100)
= $5500 + (269500/100)
= $5500 + $2695 = $8195
Thus, Amount (A) to be paid = $8195 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5500, the simple interest in 1 year
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $385 × 7 = $2695
Thus, Simple Interest (SI) = $2695
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2695
= $8195
Thus, Amount to be paid = $8195 Answer
Similar Questions
(1) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(3) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(6) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(9) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?