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) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(3) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(9) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.