Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
Correct Answer
$9775
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5750 ×7/100 × 10
= 5750 × 7 × 10/100
= 40250 × 10/100
= 402500/100
= $4025
Thus, Simple Interest = $4025
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 + $4025
= $9775
Thus, Amount to be paid = $9775 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 10)
= $5750 + ($5750 ×7/100 × 10)
= $5750 + (5750 × 7 × 10/100)
= $5750 + (40250 × 10/100)
= $5750 + (402500/100)
= $5750 + $4025 = $9775
Thus, Amount (A) to be paid = $9775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5750, the simple interest in 1 year
= 7/100 × 5750
= 7 × 5750/100
= 40250/100 = $402.5
Thus, simple interest for 1 year = $402.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $402.5 × 10 = $4025
Thus, Simple Interest (SI) = $4025
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4025
= $9775
Thus, Amount to be paid = $9775 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(10) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?