Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
Correct Answer
$6840
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 2% × 10
= $5700 ×2/100 × 10
= 5700 × 2 × 10/100
= 11400 × 10/100
= 114000/100
= $1140
Thus, Simple Interest = $1140
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 + $1140
= $6840
Thus, Amount to be paid = $6840 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 10)
= $5700 + ($5700 ×2/100 × 10)
= $5700 + (5700 × 2 × 10/100)
= $5700 + (11400 × 10/100)
= $5700 + (114000/100)
= $5700 + $1140 = $6840
Thus, Amount (A) to be paid = $6840 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 $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $114 × 10 = $1140
Thus, Simple Interest (SI) = $1140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1140
= $6840
Thus, Amount to be paid = $6840 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(6) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(10) 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.