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) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?