Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
Correct Answer
$7140
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5950 ×2/100 × 10
= 5950 × 2 × 10/100
= 11900 × 10/100
= 119000/100
= $1190
Thus, Simple Interest = $1190
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 + $1190
= $7140
Thus, Amount to be paid = $7140 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 2% × 10)
= $5950 + ($5950 ×2/100 × 10)
= $5950 + (5950 × 2 × 10/100)
= $5950 + (11900 × 10/100)
= $5950 + (119000/100)
= $5950 + $1190 = $7140
Thus, Amount (A) to be paid = $7140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5950, the simple interest in 1 year
= 2/100 × 5950
= 2 × 5950/100
= 11900/100 = $119
Thus, simple interest for 1 year = $119
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $119 × 10 = $1190
Thus, Simple Interest (SI) = $1190
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1190
= $7140
Thus, Amount to be paid = $7140 Answer
Similar Questions
(1) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(8) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.