Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
Correct Answer
$4402
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3100 ×7/100 × 6
= 3100 × 7 × 6/100
= 21700 × 6/100
= 130200/100
= $1302
Thus, Simple Interest = $1302
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 + $1302
= $4402
Thus, Amount to be paid = $4402 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 6)
= $3100 + ($3100 ×7/100 × 6)
= $3100 + (3100 × 7 × 6/100)
= $3100 + (21700 × 6/100)
= $3100 + (130200/100)
= $3100 + $1302 = $4402
Thus, Amount (A) to be paid = $4402 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $217 × 6 = $1302
Thus, Simple Interest (SI) = $1302
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1302
= $4402
Thus, Amount to be paid = $4402 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(2) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.