Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
Correct Answer
$8080
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5050 ×6/100 × 10
= 5050 × 6 × 10/100
= 30300 × 10/100
= 303000/100
= $3030
Thus, Simple Interest = $3030
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 + $3030
= $8080
Thus, Amount to be paid = $8080 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 10)
= $5050 + ($5050 ×6/100 × 10)
= $5050 + (5050 × 6 × 10/100)
= $5050 + (30300 × 10/100)
= $5050 + (303000/100)
= $5050 + $3030 = $8080
Thus, Amount (A) to be paid = $8080 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $303 × 10 = $3030
Thus, Simple Interest (SI) = $3030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3030
= $8080
Thus, Amount to be paid = $8080 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(4) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(7) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.