Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
Correct Answer
$5582.5
Solution And Explanation
Solution
Given,
Principal (P) = $3850
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) = $3850 × 9% × 5
= $3850 ×9/100 × 5
= 3850 × 9 × 5/100
= 34650 × 5/100
= 173250/100
= $1732.5
Thus, Simple Interest = $1732.5
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 = $3850 + $1732.5
= $5582.5
Thus, Amount to be paid = $5582.5 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 = $3850
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 9% × 5)
= $3850 + ($3850 ×9/100 × 5)
= $3850 + (3850 × 9 × 5/100)
= $3850 + (34650 × 5/100)
= $3850 + (173250/100)
= $3850 + $1732.5 = $5582.5
Thus, Amount (A) to be paid = $5582.5 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 $3850, the simple interest in 1 year
= 9/100 × 3850
= 9 × 3850/100
= 34650/100 = $346.5
Thus, simple interest for 1 year = $346.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $346.5 × 5 = $1732.5
Thus, Simple Interest (SI) = $1732.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1732.5
= $5582.5
Thus, Amount to be paid = $5582.5 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(5) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(7) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(9) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?