Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
Correct Answer
$3286
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 3 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% × 3
= $3100 ×2/100 × 3
= 3100 × 2 × 3/100
= 6200 × 3/100
= 18600/100
= $186
Thus, Simple Interest = $186
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 + $186
= $3286
Thus, Amount to be paid = $3286 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) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 3)
= $3100 + ($3100 ×2/100 × 3)
= $3100 + (3100 × 2 × 3/100)
= $3100 + (6200 × 3/100)
= $3100 + (18600/100)
= $3100 + $186 = $3286
Thus, Amount (A) to be paid = $3286 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 3 years
= Simple interest for 1 year × 3
= $62 × 3 = $186
Thus, Simple Interest (SI) = $186
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $186
= $3286
Thus, Amount to be paid = $3286 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.