Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
Correct Answer
$8585
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5050 ×10/100 × 7
= 5050 × 10 × 7/100
= 50500 × 7/100
= 353500/100
= $3535
Thus, Simple Interest = $3535
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 + $3535
= $8585
Thus, Amount to be paid = $8585 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) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 7)
= $5050 + ($5050 ×10/100 × 7)
= $5050 + (5050 × 10 × 7/100)
= $5050 + (50500 × 7/100)
= $5050 + (353500/100)
= $5050 + $3535 = $8585
Thus, Amount (A) to be paid = $8585 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 7 years
= Simple interest for 1 year × 7
= $505 × 7 = $3535
Thus, Simple Interest (SI) = $3535
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3535
= $8585
Thus, Amount to be paid = $8585 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(2) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.