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) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(7) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.