Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
Correct Answer
$7526
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5300 ×6/100 × 7
= 5300 × 6 × 7/100
= 31800 × 7/100
= 222600/100
= $2226
Thus, Simple Interest = $2226
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 + $2226
= $7526
Thus, Amount to be paid = $7526 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 7)
= $5300 + ($5300 ×6/100 × 7)
= $5300 + (5300 × 6 × 7/100)
= $5300 + (31800 × 7/100)
= $5300 + (222600/100)
= $5300 + $2226 = $7526
Thus, Amount (A) to be paid = $7526 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5300, the simple interest in 1 year
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = $318
Thus, simple interest for 1 year = $318
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $318 × 7 = $2226
Thus, Simple Interest (SI) = $2226
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2226
= $7526
Thus, Amount to be paid = $7526 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(3) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) 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?
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(9) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.