Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
Correct Answer
$8034
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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% × 7
= $5150 ×8/100 × 7
= 5150 × 8 × 7/100
= 41200 × 7/100
= 288400/100
= $2884
Thus, Simple Interest = $2884
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 + $2884
= $8034
Thus, Amount to be paid = $8034 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) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 7)
= $5150 + ($5150 ×8/100 × 7)
= $5150 + (5150 × 8 × 7/100)
= $5150 + (41200 × 7/100)
= $5150 + (288400/100)
= $5150 + $2884 = $8034
Thus, Amount (A) to be paid = $8034 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 7 years
= Simple interest for 1 year × 7
= $412 × 7 = $2884
Thus, Simple Interest (SI) = $2884
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2884
= $8034
Thus, Amount to be paid = $8034 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(2) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(7) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.