Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
Correct Answer
$4774
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6
= $3100 ×9/100 × 6
= 3100 × 9 × 6/100
= 27900 × 6/100
= 167400/100
= $1674
Thus, Simple Interest = $1674
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 + $1674
= $4774
Thus, Amount to be paid = $4774 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) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 6)
= $3100 + ($3100 ×9/100 × 6)
= $3100 + (3100 × 9 × 6/100)
= $3100 + (27900 × 6/100)
= $3100 + (167400/100)
= $3100 + $1674 = $4774
Thus, Amount (A) to be paid = $4774 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $279 × 6 = $1674
Thus, Simple Interest (SI) = $1674
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1674
= $4774
Thus, Amount to be paid = $4774 Answer
Similar Questions
(1) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(3) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(9) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(10) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.