Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
Correct Answer
$8034
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5150 ×7/100 × 8
= 5150 × 7 × 8/100
= 36050 × 8/100
= 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 8)
= $5150 + ($5150 ×7/100 × 8)
= $5150 + (5150 × 7 × 8/100)
= $5150 + (36050 × 8/100)
= $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 = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $360.5 × 8 = $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 Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(2) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(6) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.