Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
Correct Answer
$7155
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5300 × 5% × 7
= $5300 ×5/100 × 7
= 5300 × 5 × 7/100
= 26500 × 7/100
= 185500/100
= $1855
Thus, Simple Interest = $1855
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 = $5300 + $1855
= $7155
Thus, Amount to be paid = $7155 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 = $5300
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 7)
= $5300 + ($5300 ×5/100 × 7)
= $5300 + (5300 × 5 × 7/100)
= $5300 + (26500 × 7/100)
= $5300 + (185500/100)
= $5300 + $1855 = $7155
Thus, Amount (A) to be paid = $7155 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $265 × 7 = $1855
Thus, Simple Interest (SI) = $1855
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1855
= $7155
Thus, Amount to be paid = $7155 Answer
Similar Questions
(1) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(2) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.