Question:
What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
Correct Answer
$5775
Solution And Explanation
Solution
Given,
Principal (P) = $3750
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3750 × 9% × 6
= $3750 ×9/100 × 6
= 3750 × 9 × 6/100
= 33750 × 6/100
= 202500/100
= $2025
Thus, Simple Interest = $2025
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 = $3750 + $2025
= $5775
Thus, Amount to be paid = $5775 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 = $3750
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3750 + ($3750 × 9% × 6)
= $3750 + ($3750 ×9/100 × 6)
= $3750 + (3750 × 9 × 6/100)
= $3750 + (33750 × 6/100)
= $3750 + (202500/100)
= $3750 + $2025 = $5775
Thus, Amount (A) to be paid = $5775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3750, the simple interest in 1 year
= 9/100 × 3750
= 9 × 3750/100
= 33750/100 = $337.5
Thus, simple interest for 1 year = $337.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $337.5 × 6 = $2025
Thus, Simple Interest (SI) = $2025
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3750 + $2025
= $5775
Thus, Amount to be paid = $5775 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(10) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.