Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
Correct Answer
$7878
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5050 ×7/100 × 8
= 5050 × 7 × 8/100
= 35350 × 8/100
= 282800/100
= $2828
Thus, Simple Interest = $2828
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 + $2828
= $7878
Thus, Amount to be paid = $7878 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 8)
= $5050 + ($5050 ×7/100 × 8)
= $5050 + (5050 × 7 × 8/100)
= $5050 + (35350 × 8/100)
= $5050 + (282800/100)
= $5050 + $2828 = $7878
Thus, Amount (A) to be paid = $7878 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $353.5 × 8 = $2828
Thus, Simple Interest (SI) = $2828
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2828
= $7878
Thus, Amount to be paid = $7878 Answer
Similar Questions
(1) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.