Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
Correct Answer
$4340
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 8%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 5
= $3100 ×8/100 × 5
= 3100 × 8 × 5/100
= 24800 × 5/100
= 124000/100
= $1240
Thus, Simple Interest = $1240
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 + $1240
= $4340
Thus, Amount to be paid = $4340 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) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 8% × 5)
= $3100 + ($3100 ×8/100 × 5)
= $3100 + (3100 × 8 × 5/100)
= $3100 + (24800 × 5/100)
= $3100 + (124000/100)
= $3100 + $1240 = $4340
Thus, Amount (A) to be paid = $4340 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3100, the simple interest in 1 year
= 8/100 × 3100
= 8 × 3100/100
= 24800/100 = $248
Thus, simple interest for 1 year = $248
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $248 × 5 = $1240
Thus, Simple Interest (SI) = $1240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1240
= $4340
Thus, Amount to be paid = $4340 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(5) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.