Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
Correct Answer
$10350
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5750 ×8/100 × 10
= 5750 × 8 × 10/100
= 46000 × 10/100
= 460000/100
= $4600
Thus, Simple Interest = $4600
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 + $4600
= $10350
Thus, Amount to be paid = $10350 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 10)
= $5750 + ($5750 ×8/100 × 10)
= $5750 + (5750 × 8 × 10/100)
= $5750 + (46000 × 10/100)
= $5750 + (460000/100)
= $5750 + $4600 = $10350
Thus, Amount (A) to be paid = $10350 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5750, the simple interest in 1 year
= 8/100 × 5750
= 8 × 5750/100
= 46000/100 = $460
Thus, simple interest for 1 year = $460
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $460 × 10 = $4600
Thus, Simple Interest (SI) = $4600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4600
= $10350
Thus, Amount to be paid = $10350 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(4) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(7) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.