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) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(7) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.