Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
Correct Answer
$10925
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5750 ×10/100 × 9
= 5750 × 10 × 9/100
= 57500 × 9/100
= 517500/100
= $5175
Thus, Simple Interest = $5175
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 + $5175
= $10925
Thus, Amount to be paid = $10925 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 10% × 9)
= $5750 + ($5750 ×10/100 × 9)
= $5750 + (5750 × 10 × 9/100)
= $5750 + (57500 × 9/100)
= $5750 + (517500/100)
= $5750 + $5175 = $10925
Thus, Amount (A) to be paid = $10925 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5750, the simple interest in 1 year
= 10/100 × 5750
= 10 × 5750/100
= 57500/100 = $575
Thus, simple interest for 1 year = $575
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $575 × 9 = $5175
Thus, Simple Interest (SI) = $5175
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $5175
= $10925
Thus, Amount to be paid = $10925 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(3) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(10) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.