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) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?