Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
Correct Answer
$7322.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5050 ×5/100 × 9
= 5050 × 5 × 9/100
= 25250 × 9/100
= 227250/100
= $2272.5
Thus, Simple Interest = $2272.5
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 + $2272.5
= $7322.5
Thus, Amount to be paid = $7322.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 5% × 9)
= $5050 + ($5050 ×5/100 × 9)
= $5050 + (5050 × 5 × 9/100)
= $5050 + (25250 × 9/100)
= $5050 + (227250/100)
= $5050 + $2272.5 = $7322.5
Thus, Amount (A) to be paid = $7322.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5050, the simple interest in 1 year
= 5/100 × 5050
= 5 × 5050/100
= 25250/100 = $252.5
Thus, simple interest for 1 year = $252.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $252.5 × 9 = $2272.5
Thus, Simple Interest (SI) = $2272.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2272.5
= $7322.5
Thus, Amount to be paid = $7322.5 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.