Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
Correct Answer
$6262
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5050 ×3/100 × 8
= 5050 × 3 × 8/100
= 15150 × 8/100
= 121200/100
= $1212
Thus, Simple Interest = $1212
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 + $1212
= $6262
Thus, Amount to be paid = $6262 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 8)
= $5050 + ($5050 ×3/100 × 8)
= $5050 + (5050 × 3 × 8/100)
= $5050 + (15150 × 8/100)
= $5050 + (121200/100)
= $5050 + $1212 = $6262
Thus, Amount (A) to be paid = $6262 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $151.5 × 8 = $1212
Thus, Simple Interest (SI) = $1212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1212
= $6262
Thus, Amount to be paid = $6262 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(2) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(4) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(9) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?