Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
Correct Answer
$9785
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5150 × 9% × 10
= $5150 ×9/100 × 10
= 5150 × 9 × 10/100
= 46350 × 10/100
= 463500/100
= $4635
Thus, Simple Interest = $4635
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 = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 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 = $5150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 10)
= $5150 + ($5150 ×9/100 × 10)
= $5150 + (5150 × 9 × 10/100)
= $5150 + (46350 × 10/100)
= $5150 + (463500/100)
= $5150 + $4635 = $9785
Thus, Amount (A) to be paid = $9785 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $463.5 × 10 = $4635
Thus, Simple Interest (SI) = $4635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 Answer
Similar Questions
(1) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(10) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.