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) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(3) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.