Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
Correct Answer
$4960
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3100 ×10/100 × 6
= 3100 × 10 × 6/100
= 31000 × 6/100
= 186000/100
= $1860
Thus, Simple Interest = $1860
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 + $1860
= $4960
Thus, Amount to be paid = $4960 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 10% × 6)
= $3100 + ($3100 ×10/100 × 6)
= $3100 + (3100 × 10 × 6/100)
= $3100 + (31000 × 6/100)
= $3100 + (186000/100)
= $3100 + $1860 = $4960
Thus, Amount (A) to be paid = $4960 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3100, the simple interest in 1 year
= 10/100 × 3100
= 10 × 3100/100
= 31000/100 = $310
Thus, simple interest for 1 year = $310
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $310 × 6 = $1860
Thus, Simple Interest (SI) = $1860
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1860
= $4960
Thus, Amount to be paid = $4960 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(5) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(8) 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.
(9) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.