Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.
Correct Answer
$6666
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5050 × 4% × 8
= $5050 ×4/100 × 8
= 5050 × 4 × 8/100
= 20200 × 8/100
= 161600/100
= $1616
Thus, Simple Interest = $1616
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 = $5050 + $1616
= $6666
Thus, Amount to be paid = $6666 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 = $5050
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 4% × 8)
= $5050 + ($5050 ×4/100 × 8)
= $5050 + (5050 × 4 × 8/100)
= $5050 + (20200 × 8/100)
= $5050 + (161600/100)
= $5050 + $1616 = $6666
Thus, Amount (A) to be paid = $6666 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5050, the simple interest in 1 year
= 4/100 × 5050
= 4 × 5050/100
= 20200/100 = $202
Thus, simple interest for 1 year = $202
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $202 × 8 = $1616
Thus, Simple Interest (SI) = $1616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1616
= $6666
Thus, Amount to be paid = $6666 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(8) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(10) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.