Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
Correct Answer
$10830
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5700 ×9/100 × 10
= 5700 × 9 × 10/100
= 51300 × 10/100
= 513000/100
= $5130
Thus, Simple Interest = $5130
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 + $5130
= $10830
Thus, Amount to be paid = $10830 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 10)
= $5700 + ($5700 ×9/100 × 10)
= $5700 + (5700 × 9 × 10/100)
= $5700 + (51300 × 10/100)
= $5700 + (513000/100)
= $5700 + $5130 = $10830
Thus, Amount (A) to be paid = $10830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5700, the simple interest in 1 year
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = $513
Thus, simple interest for 1 year = $513
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $513 × 10 = $5130
Thus, Simple Interest (SI) = $5130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(6) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(10) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.