Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
Correct Answer
$7242
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 6% × 7
= $5100 ×6/100 × 7
= 5100 × 6 × 7/100
= 30600 × 7/100
= 214200/100
= $2142
Thus, Simple Interest = $2142
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 = $5100 + $2142
= $7242
Thus, Amount to be paid = $7242 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 = $5100
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 7)
= $5100 + ($5100 ×6/100 × 7)
= $5100 + (5100 × 6 × 7/100)
= $5100 + (30600 × 7/100)
= $5100 + (214200/100)
= $5100 + $2142 = $7242
Thus, Amount (A) to be paid = $7242 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 $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $306 × 7 = $2142
Thus, Simple Interest (SI) = $2142
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2142
= $7242
Thus, Amount to be paid = $7242 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?