Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
Correct Answer
$9372.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5750 ×7/100 × 9
= 5750 × 7 × 9/100
= 40250 × 9/100
= 362250/100
= $3622.5
Thus, Simple Interest = $3622.5
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 + $3622.5
= $9372.5
Thus, Amount to be paid = $9372.5 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 9)
= $5750 + ($5750 ×7/100 × 9)
= $5750 + (5750 × 7 × 9/100)
= $5750 + (40250 × 9/100)
= $5750 + (362250/100)
= $5750 + $3622.5 = $9372.5
Thus, Amount (A) to be paid = $9372.5 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 9 years
= Simple interest for 1 year × 9
= $402.5 × 9 = $3622.5
Thus, Simple Interest (SI) = $3622.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3622.5
= $9372.5
Thus, Amount to be paid = $9372.5 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(9) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.