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) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(4) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.
(6) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.