Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
Correct Answer
$7080
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 2% × 10
= $5900 ×2/100 × 10
= 5900 × 2 × 10/100
= 11800 × 10/100
= 118000/100
= $1180
Thus, Simple Interest = $1180
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 = $5900 + $1180
= $7080
Thus, Amount to be paid = $7080 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 = $5900
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 2% × 10)
= $5900 + ($5900 ×2/100 × 10)
= $5900 + (5900 × 2 × 10/100)
= $5900 + (11800 × 10/100)
= $5900 + (118000/100)
= $5900 + $1180 = $7080
Thus, Amount (A) to be paid = $7080 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 $5900, the simple interest in 1 year
= 2/100 × 5900
= 2 × 5900/100
= 11800/100 = $118
Thus, simple interest for 1 year = $118
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $118 × 10 = $1180
Thus, Simple Interest (SI) = $1180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1180
= $7080
Thus, Amount to be paid = $7080 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.