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) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(6) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?