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) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.