Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
Correct Answer
$4927.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 7%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3650 × 7% × 5
= $3650 ×7/100 × 5
= 3650 × 7 × 5/100
= 25550 × 5/100
= 127750/100
= $1277.5
Thus, Simple Interest = $1277.5
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 = $3650 + $1277.5
= $4927.5
Thus, Amount to be paid = $4927.5 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 = $3650
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 7% × 5)
= $3650 + ($3650 ×7/100 × 5)
= $3650 + (3650 × 7 × 5/100)
= $3650 + (25550 × 5/100)
= $3650 + (127750/100)
= $3650 + $1277.5 = $4927.5
Thus, Amount (A) to be paid = $4927.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3650, the simple interest in 1 year
= 7/100 × 3650
= 7 × 3650/100
= 25550/100 = $255.5
Thus, simple interest for 1 year = $255.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $255.5 × 5 = $1277.5
Thus, Simple Interest (SI) = $1277.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1277.5
= $4927.5
Thus, Amount to be paid = $4927.5 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(8) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(9) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.