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 Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.