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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(3) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.