Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?
Correct Answer
$5655
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 9%
Time (t) = 5 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) = $3900 × 9% × 5
= $3900 ×9/100 × 5
= 3900 × 9 × 5/100
= 35100 × 5/100
= 175500/100
= $1755
Thus, Simple Interest = $1755
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 = $3900 + $1755
= $5655
Thus, Amount to be paid = $5655 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 = $3900
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 9% × 5)
= $3900 + ($3900 ×9/100 × 5)
= $3900 + (3900 × 9 × 5/100)
= $3900 + (35100 × 5/100)
= $3900 + (175500/100)
= $3900 + $1755 = $5655
Thus, Amount (A) to be paid = $5655 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 $3900, the simple interest in 1 year
= 9/100 × 3900
= 9 × 3900/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $351 × 5 = $1755
Thus, Simple Interest (SI) = $1755
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1755
= $5655
Thus, Amount to be paid = $5655 Answer
Similar Questions
(1) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(5) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.