Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
Correct Answer
$3410
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 5
= $3100 ×2/100 × 5
= 3100 × 2 × 5/100
= 6200 × 5/100
= 31000/100
= $310
Thus, Simple Interest = $310
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 + $310
= $3410
Thus, Amount to be paid = $3410 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) = 2%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 5)
= $3100 + ($3100 ×2/100 × 5)
= $3100 + (3100 × 2 × 5/100)
= $3100 + (6200 × 5/100)
= $3100 + (31000/100)
= $3100 + $310 = $3410
Thus, Amount (A) to be paid = $3410 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3100, the simple interest in 1 year
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = $62
Thus, simple interest for 1 year = $62
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $62 × 5 = $310
Thus, Simple Interest (SI) = $310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $310
= $3410
Thus, Amount to be paid = $3410 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?