Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
Correct Answer
$6785
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5750 ×2/100 × 9
= 5750 × 2 × 9/100
= 11500 × 9/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 + $1035
= $6785
Thus, Amount to be paid = $6785 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 2% × 9)
= $5750 + ($5750 ×2/100 × 9)
= $5750 + (5750 × 2 × 9/100)
= $5750 + (11500 × 9/100)
= $5750 + (103500/100)
= $5750 + $1035 = $6785
Thus, Amount (A) to be paid = $6785 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5750, the simple interest in 1 year
= 2/100 × 5750
= 2 × 5750/100
= 11500/100 = $115
Thus, simple interest for 1 year = $115
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $115 × 9 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1035
= $6785
Thus, Amount to be paid = $6785 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.