Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
Correct Answer
$8639
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 7
= $5300 ×9/100 × 7
= 5300 × 9 × 7/100
= 47700 × 7/100
= 333900/100
= $3339
Thus, Simple Interest = $3339
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 + $3339
= $8639
Thus, Amount to be paid = $8639 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 7)
= $5300 + ($5300 ×9/100 × 7)
= $5300 + (5300 × 9 × 7/100)
= $5300 + (47700 × 7/100)
= $5300 + (333900/100)
= $5300 + $3339 = $8639
Thus, Amount (A) to be paid = $8639 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $477 × 7 = $3339
Thus, Simple Interest (SI) = $3339
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3339
= $8639
Thus, Amount to be paid = $8639 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(3) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(8) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.