Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
Correct Answer
$6413
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5300 ×3/100 × 7
= 5300 × 3 × 7/100
= 15900 × 7/100
= 111300/100
= $1113
Thus, Simple Interest = $1113
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 + $1113
= $6413
Thus, Amount to be paid = $6413 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 7)
= $5300 + ($5300 ×3/100 × 7)
= $5300 + (5300 × 3 × 7/100)
= $5300 + (15900 × 7/100)
= $5300 + (111300/100)
= $5300 + $1113 = $6413
Thus, Amount (A) to be paid = $6413 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $159 × 7 = $1113
Thus, Simple Interest (SI) = $1113
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1113
= $6413
Thus, Amount to be paid = $6413 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(9) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(10) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?