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) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(3) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.