Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
Correct Answer
$7004
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5150 ×4/100 × 9
= 5150 × 4 × 9/100
= 20600 × 9/100
= 185400/100
= $1854
Thus, Simple Interest = $1854
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 + $1854
= $7004
Thus, Amount to be paid = $7004 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 9)
= $5150 + ($5150 ×4/100 × 9)
= $5150 + (5150 × 4 × 9/100)
= $5150 + (20600 × 9/100)
= $5150 + (185400/100)
= $5150 + $1854 = $7004
Thus, Amount (A) to be paid = $7004 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $206 × 9 = $1854
Thus, Simple Interest (SI) = $1854
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1854
= $7004
Thus, Amount to be paid = $7004 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(2) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(6) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(8) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.