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) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(2) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(9) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.