Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
Correct Answer
$7878
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5050 ×8/100 × 7
= 5050 × 8 × 7/100
= 40400 × 7/100
= 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 8% × 7)
= $5050 + ($5050 ×8/100 × 7)
= $5050 + (5050 × 8 × 7/100)
= $5050 + (40400 × 7/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5050, the simple interest in 1 year
= 8/100 × 5050
= 8 × 5050/100
= 40400/100 = $404
Thus, simple interest for 1 year = $404
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $404 × 7 = $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) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
(4) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.