Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
Correct Answer
$7475
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5750 × 3% × 10
= $5750 ×3/100 × 10
= 5750 × 3 × 10/100
= 17250 × 10/100
= 172500/100
= $1725
Thus, Simple Interest = $1725
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 = $5750 + $1725
= $7475
Thus, Amount to be paid = $7475 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 = $5750
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 10)
= $5750 + ($5750 ×3/100 × 10)
= $5750 + (5750 × 3 × 10/100)
= $5750 + (17250 × 10/100)
= $5750 + (172500/100)
= $5750 + $1725 = $7475
Thus, Amount (A) to be paid = $7475 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 $5750, the simple interest in 1 year
= 3/100 × 5750
= 3 × 5750/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $172.5 × 10 = $1725
Thus, Simple Interest (SI) = $1725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1725
= $7475
Thus, Amount to be paid = $7475 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(5) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.