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) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(3) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.