Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
Correct Answer
$9209.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 7
= $5650 ×9/100 × 7
= 5650 × 9 × 7/100
= 50850 × 7/100
= 355950/100
= $3559.5
Thus, Simple Interest = $3559.5
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 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 7)
= $5650 + ($5650 ×9/100 × 7)
= $5650 + (5650 × 9 × 7/100)
= $5650 + (50850 × 7/100)
= $5650 + (355950/100)
= $5650 + $3559.5 = $9209.5
Thus, Amount (A) to be paid = $9209.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $508.5 × 7 = $3559.5
Thus, Simple Interest (SI) = $3559.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(5) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(8) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.