Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
Correct Answer
$7302.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 3% × 9
= $5750 ×3/100 × 9
= 5750 × 3 × 9/100
= 17250 × 9/100
= 155250/100
= $1552.5
Thus, Simple Interest = $1552.5
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 + $1552.5
= $7302.5
Thus, Amount to be paid = $7302.5 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) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 9)
= $5750 + ($5750 ×3/100 × 9)
= $5750 + (5750 × 3 × 9/100)
= $5750 + (17250 × 9/100)
= $5750 + (155250/100)
= $5750 + $1552.5 = $7302.5
Thus, Amount (A) to be paid = $7302.5 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 9 years
= Simple interest for 1 year × 9
= $172.5 × 9 = $1552.5
Thus, Simple Interest (SI) = $1552.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1552.5
= $7302.5
Thus, Amount to be paid = $7302.5 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.