Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
Correct Answer
$9282
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 7% × 8
= $5950 ×7/100 × 8
= 5950 × 7 × 8/100
= 41650 × 8/100
= 333200/100
= $3332
Thus, Simple Interest = $3332
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 = $5950 + $3332
= $9282
Thus, Amount to be paid = $9282 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 = $5950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 8)
= $5950 + ($5950 ×7/100 × 8)
= $5950 + (5950 × 7 × 8/100)
= $5950 + (41650 × 8/100)
= $5950 + (333200/100)
= $5950 + $3332 = $9282
Thus, Amount (A) to be paid = $9282 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 $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416.5 × 8 = $3332
Thus, Simple Interest (SI) = $3332
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3332
= $9282
Thus, Amount to be paid = $9282 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(2) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.