Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
Correct Answer
$9595
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5050 ×10/100 × 9
= 5050 × 10 × 9/100
= 50500 × 9/100
= 454500/100
= $4545
Thus, Simple Interest = $4545
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 + $4545
= $9595
Thus, Amount to be paid = $9595 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 9)
= $5050 + ($5050 ×10/100 × 9)
= $5050 + (5050 × 10 × 9/100)
= $5050 + (50500 × 9/100)
= $5050 + (454500/100)
= $5050 + $4545 = $9595
Thus, Amount (A) to be paid = $9595 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5050, the simple interest in 1 year
= 10/100 × 5050
= 10 × 5050/100
= 50500/100 = $505
Thus, simple interest for 1 year = $505
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $505 × 9 = $4545
Thus, Simple Interest (SI) = $4545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4545
= $9595
Thus, Amount to be paid = $9595 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(6) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 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 2% simple interest for 8 years.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.