Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
Correct Answer
$9200
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5750 ×6/100 × 10
= 5750 × 6 × 10/100
= 34500 × 10/100
= 345000/100
= $3450
Thus, Simple Interest = $3450
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 + $3450
= $9200
Thus, Amount to be paid = $9200 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 10)
= $5750 + ($5750 ×6/100 × 10)
= $5750 + (5750 × 6 × 10/100)
= $5750 + (34500 × 10/100)
= $5750 + (345000/100)
= $5750 + $3450 = $9200
Thus, Amount (A) to be paid = $9200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5750, the simple interest in 1 year
= 6/100 × 5750
= 6 × 5750/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $345 × 10 = $3450
Thus, Simple Interest (SI) = $3450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3450
= $9200
Thus, Amount to be paid = $9200 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(4) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(10) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.