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) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.