Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?
Correct Answer
$3844
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 4%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 6
= $3100 ×4/100 × 6
= 3100 × 4 × 6/100
= 12400 × 6/100
= 74400/100
= $744
Thus, Simple Interest = $744
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 + $744
= $3844
Thus, Amount to be paid = $3844 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) = 4%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 4% × 6)
= $3100 + ($3100 ×4/100 × 6)
= $3100 + (3100 × 4 × 6/100)
= $3100 + (12400 × 6/100)
= $3100 + (74400/100)
= $3100 + $744 = $3844
Thus, Amount (A) to be paid = $3844 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3100, the simple interest in 1 year
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = $124
Thus, simple interest for 1 year = $124
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $124 × 6 = $744
Thus, Simple Interest (SI) = $744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $744
= $3844
Thus, Amount to be paid = $3844 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(3) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(10) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.