Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
Correct Answer
$8192.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 5% × 9
= $5650 ×5/100 × 9
= 5650 × 5 × 9/100
= 28250 × 9/100
= 254250/100
= $2542.5
Thus, Simple Interest = $2542.5
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 = $5650 + $2542.5
= $8192.5
Thus, Amount to be paid = $8192.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 9)
= $5650 + ($5650 ×5/100 × 9)
= $5650 + (5650 × 5 × 9/100)
= $5650 + (28250 × 9/100)
= $5650 + (254250/100)
= $5650 + $2542.5 = $8192.5
Thus, Amount (A) to be paid = $8192.5 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 $5650, the simple interest in 1 year
= 5/100 × 5650
= 5 × 5650/100
= 28250/100 = $282.5
Thus, simple interest for 1 year = $282.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $282.5 × 9 = $2542.5
Thus, Simple Interest (SI) = $2542.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2542.5
= $8192.5
Thus, Amount to be paid = $8192.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(3) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(8) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.