Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
Correct Answer
$7735
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5950 ×3/100 × 10
= 5950 × 3 × 10/100
= 17850 × 10/100
= 178500/100
= $1785
Thus, Simple Interest = $1785
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 + $1785
= $7735
Thus, Amount to be paid = $7735 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 3% × 10)
= $5950 + ($5950 ×3/100 × 10)
= $5950 + (5950 × 3 × 10/100)
= $5950 + (17850 × 10/100)
= $5950 + (178500/100)
= $5950 + $1785 = $7735
Thus, Amount (A) to be paid = $7735 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5950, the simple interest in 1 year
= 3/100 × 5950
= 3 × 5950/100
= 17850/100 = $178.5
Thus, simple interest for 1 year = $178.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $178.5 × 10 = $1785
Thus, Simple Interest (SI) = $1785
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1785
= $7735
Thus, Amount to be paid = $7735 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.