Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
Correct Answer
$8550
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5700 × 5% × 10
= $5700 ×5/100 × 10
= 5700 × 5 × 10/100
= 28500 × 10/100
= 285000/100
= $2850
Thus, Simple Interest = $2850
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 = $5700 + $2850
= $8550
Thus, Amount to be paid = $8550 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 = $5700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 10)
= $5700 + ($5700 ×5/100 × 10)
= $5700 + (5700 × 5 × 10/100)
= $5700 + (28500 × 10/100)
= $5700 + (285000/100)
= $5700 + $2850 = $8550
Thus, Amount (A) to be paid = $8550 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $285 × 10 = $2850
Thus, Simple Interest (SI) = $2850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2850
= $8550
Thus, Amount to be paid = $8550 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(4) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?