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) Betty had to pay $4505 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 Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(6) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.