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) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(2) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(5) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?