Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
Correct Answer
$8410
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5800 × 5% × 9
= $5800 ×5/100 × 9
= 5800 × 5 × 9/100
= 29000 × 9/100
= 261000/100
= $2610
Thus, Simple Interest = $2610
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 = $5800 + $2610
= $8410
Thus, Amount to be paid = $8410 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 = $5800
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 5% × 9)
= $5800 + ($5800 ×5/100 × 9)
= $5800 + (5800 × 5 × 9/100)
= $5800 + (29000 × 9/100)
= $5800 + (261000/100)
= $5800 + $2610 = $8410
Thus, Amount (A) to be paid = $8410 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 $5800, the simple interest in 1 year
= 5/100 × 5800
= 5 × 5800/100
= 29000/100 = $290
Thus, simple interest for 1 year = $290
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $290 × 9 = $2610
Thus, Simple Interest (SI) = $2610
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2610
= $8410
Thus, Amount to be paid = $8410 Answer
Similar Questions
(1) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(5) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(9) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(10) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.