Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
Correct Answer
$4562.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3650 × 5% × 5
= $3650 ×5/100 × 5
= 3650 × 5 × 5/100
= 18250 × 5/100
= 91250/100
= $912.5
Thus, Simple Interest = $912.5
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 + $912.5
= $4562.5
Thus, Amount to be paid = $4562.5 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 5)
= $3650 + ($3650 ×5/100 × 5)
= $3650 + (3650 × 5 × 5/100)
= $3650 + (18250 × 5/100)
= $3650 + (91250/100)
= $3650 + $912.5 = $4562.5
Thus, Amount (A) to be paid = $4562.5 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 $3650, the simple interest in 1 year
= 5/100 × 3650
= 5 × 3650/100
= 18250/100 = $182.5
Thus, simple interest for 1 year = $182.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $182.5 × 5 = $912.5
Thus, Simple Interest (SI) = $912.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $912.5
= $4562.5
Thus, Amount to be paid = $4562.5 Answer
Similar Questions
(1) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.