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) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(6) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(8) 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?
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?
(10) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?