Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
Correct Answer
$6732
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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) = $5100 × 4% × 8
= $5100 ×4/100 × 8
= 5100 × 4 × 8/100
= 20400 × 8/100
= 163200/100
= $1632
Thus, Simple Interest = $1632
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 + $1632
= $6732
Thus, Amount to be paid = $6732 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 8)
= $5100 + ($5100 ×4/100 × 8)
= $5100 + (5100 × 4 × 8/100)
= $5100 + (20400 × 8/100)
= $5100 + (163200/100)
= $5100 + $1632 = $6732
Thus, Amount (A) to be paid = $6732 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 $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $204 × 8 = $1632
Thus, Simple Interest (SI) = $1632
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1632
= $6732
Thus, Amount to be paid = $6732 Answer
Similar Questions
(1) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.