Question:
If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3224
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 2 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% × 2
= $3100 ×2/100 × 2
= 3100 × 2 × 2/100
= 6200 × 2/100
= 12400/100
= $124
Thus, Simple Interest = $124
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 + $124
= $3224
Thus, Amount to be paid = $3224 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) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 2)
= $3100 + ($3100 ×2/100 × 2)
= $3100 + (3100 × 2 × 2/100)
= $3100 + (6200 × 2/100)
= $3100 + (12400/100)
= $3100 + $124 = $3224
Thus, Amount (A) to be paid = $3224 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 in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3100, the simple interest in 1 year
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = $62
Thus, simple interest in 1 year = $62
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $62 × 2 = $124
Thus, Simple Interest (SI) = $124
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $124
= $3224
Thus, Amount to be paid = $3224 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.