Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
Correct Answer
$6784
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5300 ×4/100 × 7
= 5300 × 4 × 7/100
= 21200 × 7/100
= 148400/100
= $1484
Thus, Simple Interest = $1484
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 + $1484
= $6784
Thus, Amount to be paid = $6784 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 7)
= $5300 + ($5300 ×4/100 × 7)
= $5300 + (5300 × 4 × 7/100)
= $5300 + (21200 × 7/100)
= $5300 + (148400/100)
= $5300 + $1484 = $6784
Thus, Amount (A) to be paid = $6784 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $212 × 7 = $1484
Thus, Simple Interest (SI) = $1484
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1484
= $6784
Thus, Amount to be paid = $6784 Answer
Similar Questions
(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(3) 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.
(4) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.