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) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.