Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
Correct Answer
$10115
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5950 ×10/100 × 7
= 5950 × 10 × 7/100
= 59500 × 7/100
= 416500/100
= $4165
Thus, Simple Interest = $4165
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 + $4165
= $10115
Thus, Amount to be paid = $10115 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 10% × 7)
= $5950 + ($5950 ×10/100 × 7)
= $5950 + (5950 × 10 × 7/100)
= $5950 + (59500 × 7/100)
= $5950 + (416500/100)
= $5950 + $4165 = $10115
Thus, Amount (A) to be paid = $10115 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5950, the simple interest in 1 year
= 10/100 × 5950
= 10 × 5950/100
= 59500/100 = $595
Thus, simple interest for 1 year = $595
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $595 × 7 = $4165
Thus, Simple Interest (SI) = $4165
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4165
= $10115
Thus, Amount to be paid = $10115 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(7) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.