Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3100 × 10% × 5
= $3100 ×10/100 × 5
= 3100 × 10 × 5/100
= 31000 × 5/100
= 155000/100
= $1550
Thus, Simple Interest = $1550
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 = $3100 + $1550
= $4650
Thus, Amount to be paid = $4650 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 = $3100
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 10% × 5)
= $3100 + ($3100 ×10/100 × 5)
= $3100 + (3100 × 10 × 5/100)
= $3100 + (31000 × 5/100)
= $3100 + (155000/100)
= $3100 + $1550 = $4650
Thus, Amount (A) to be paid = $4650 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3100, the simple interest in 1 year
= 10/100 × 3100
= 10 × 3100/100
= 31000/100 = $310
Thus, simple interest for 1 year = $310
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $310 × 5 = $1550
Thus, Simple Interest (SI) = $1550
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1550
= $4650
Thus, Amount to be paid = $4650 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(6) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.