Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
Correct Answer
$7171
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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% × 7
= $5050 ×6/100 × 7
= 5050 × 6 × 7/100
= 30300 × 7/100
= 212100/100
= $2121
Thus, Simple Interest = $2121
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 + $2121
= $7171
Thus, Amount to be paid = $7171 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) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 7)
= $5050 + ($5050 ×6/100 × 7)
= $5050 + (5050 × 6 × 7/100)
= $5050 + (30300 × 7/100)
= $5050 + (212100/100)
= $5050 + $2121 = $7171
Thus, Amount (A) to be paid = $7171 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 7 years
= Simple interest for 1 year × 7
= $303 × 7 = $2121
Thus, Simple Interest (SI) = $2121
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2121
= $7171
Thus, Amount to be paid = $7171 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(4) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(9) If Robert paid $3720 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 does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?