Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
Correct Answer
$11900
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5950 ×10/100 × 10
= 5950 × 10 × 10/100
= 59500 × 10/100
= 595000/100
= $5950
Thus, Simple Interest = $5950
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 + $5950
= $11900
Thus, Amount to be paid = $11900 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) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 10% × 10)
= $5950 + ($5950 ×10/100 × 10)
= $5950 + (5950 × 10 × 10/100)
= $5950 + (59500 × 10/100)
= $5950 + (595000/100)
= $5950 + $5950 = $11900
Thus, Amount (A) to be paid = $11900 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 10 years
= Simple interest for 1 year × 10
= $595 × 10 = $5950
Thus, Simple Interest (SI) = $5950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $5950
= $11900
Thus, Amount to be paid = $11900 Answer
Similar Questions
(1) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(3) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(4) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(7) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.