Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
Correct Answer
$6612
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 8
= $5700 ×2/100 × 8
= 5700 × 2 × 8/100
= 11400 × 8/100
= 91200/100
= $912
Thus, Simple Interest = $912
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 = $5700 + $912
= $6612
Thus, Amount to be paid = $6612 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 8)
= $5700 + ($5700 ×2/100 × 8)
= $5700 + (5700 × 2 × 8/100)
= $5700 + (11400 × 8/100)
= $5700 + (91200/100)
= $5700 + $912 = $6612
Thus, Amount (A) to be paid = $6612 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $114 × 8 = $912
Thus, Simple Interest (SI) = $912
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $912
= $6612
Thus, Amount to be paid = $6612 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(10) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?