Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
Correct Answer
$8446
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5150 ×8/100 × 8
= 5150 × 8 × 8/100
= 41200 × 8/100
= 329600/100
= $3296
Thus, Simple Interest = $3296
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 + $3296
= $8446
Thus, Amount to be paid = $8446 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 8)
= $5150 + ($5150 ×8/100 × 8)
= $5150 + (5150 × 8 × 8/100)
= $5150 + (41200 × 8/100)
= $5150 + (329600/100)
= $5150 + $3296 = $8446
Thus, Amount (A) to be paid = $8446 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $412 × 8 = $3296
Thus, Simple Interest (SI) = $3296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3296
= $8446
Thus, Amount to be paid = $8446 Answer
Similar Questions
(1) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.
(4) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(9) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.