Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
Correct Answer
$9282
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 8% × 7
= $5950 ×8/100 × 7
= 5950 × 8 × 7/100
= 47600 × 7/100
= 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 8% × 7)
= $5950 + ($5950 ×8/100 × 7)
= $5950 + (5950 × 8 × 7/100)
= $5950 + (47600 × 7/100)
= $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 = 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 $5950, the simple interest in 1 year
= 8/100 × 5950
= 8 × 5950/100
= 47600/100 = $476
Thus, simple interest for 1 year = $476
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $476 × 7 = $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) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(4) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(8) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.