Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
Correct Answer
$7239
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5700 ×3/100 × 9
= 5700 × 3 × 9/100
= 17100 × 9/100
= 153900/100
= $1539
Thus, Simple Interest = $1539
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 + $1539
= $7239
Thus, Amount to be paid = $7239 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 9)
= $5700 + ($5700 ×3/100 × 9)
= $5700 + (5700 × 3 × 9/100)
= $5700 + (17100 × 9/100)
= $5700 + (153900/100)
= $5700 + $1539 = $7239
Thus, Amount (A) to be paid = $7239 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $171 × 9 = $1539
Thus, Simple Interest (SI) = $1539
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1539
= $7239
Thus, Amount to be paid = $7239 Answer
Similar Questions
(1) 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?
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(5) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.