Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
Correct Answer
$9321.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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% × 9
= $5150 ×9/100 × 9
= 5150 × 9 × 9/100
= 46350 × 9/100
= 417150/100
= $4171.5
Thus, Simple Interest = $4171.5
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 = $5150 + $4171.5
= $9321.5
Thus, Amount to be paid = $9321.5 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 = $5150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 9)
= $5150 + ($5150 ×9/100 × 9)
= $5150 + (5150 × 9 × 9/100)
= $5150 + (46350 × 9/100)
= $5150 + (417150/100)
= $5150 + $4171.5 = $9321.5
Thus, Amount (A) to be paid = $9321.5 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 9 years
= Simple interest for 1 year × 9
= $463.5 × 9 = $4171.5
Thus, Simple Interest (SI) = $4171.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4171.5
= $9321.5
Thus, Amount to be paid = $9321.5 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(4) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(8) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(10) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.