Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
Correct Answer
$5475
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3650 ×10/100 × 5
= 3650 × 10 × 5/100
= 36500 × 5/100
= 182500/100
= $1825
Thus, Simple Interest = $1825
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 + $1825
= $5475
Thus, Amount to be paid = $5475 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 10% × 5)
= $3650 + ($3650 ×10/100 × 5)
= $3650 + (3650 × 10 × 5/100)
= $3650 + (36500 × 5/100)
= $3650 + (182500/100)
= $3650 + $1825 = $5475
Thus, Amount (A) to be paid = $5475 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3650, the simple interest in 1 year
= 10/100 × 3650
= 10 × 3650/100
= 36500/100 = $365
Thus, simple interest for 1 year = $365
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $365 × 5 = $1825
Thus, Simple Interest (SI) = $1825
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1825
= $5475
Thus, Amount to be paid = $5475 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.