Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
Correct Answer
$6171
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 3% × 7
= $5100 ×3/100 × 7
= 5100 × 3 × 7/100
= 15300 × 7/100
= 107100/100
= $1071
Thus, Simple Interest = $1071
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 + $1071
= $6171
Thus, Amount to be paid = $6171 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 3% × 7)
= $5100 + ($5100 ×3/100 × 7)
= $5100 + (5100 × 3 × 7/100)
= $5100 + (15300 × 7/100)
= $5100 + (107100/100)
= $5100 + $1071 = $6171
Thus, Amount (A) to be paid = $6171 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 $5100, the simple interest in 1 year
= 3/100 × 5100
= 3 × 5100/100
= 15300/100 = $153
Thus, simple interest for 1 year = $153
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $153 × 7 = $1071
Thus, Simple Interest (SI) = $1071
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1071
= $6171
Thus, Amount to be paid = $6171 Answer
Similar Questions
(1) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.