Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
Correct Answer
$4745
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 6%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 5
= $3650 ×6/100 × 5
= 3650 × 6 × 5/100
= 21900 × 5/100
= 109500/100
= $1095
Thus, Simple Interest = $1095
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 + $1095
= $4745
Thus, Amount to be paid = $4745 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) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 6% × 5)
= $3650 + ($3650 ×6/100 × 5)
= $3650 + (3650 × 6 × 5/100)
= $3650 + (21900 × 5/100)
= $3650 + (109500/100)
= $3650 + $1095 = $4745
Thus, Amount (A) to be paid = $4745 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3650, the simple interest in 1 year
= 6/100 × 3650
= 6 × 3650/100
= 21900/100 = $219
Thus, simple interest for 1 year = $219
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $219 × 5 = $1095
Thus, Simple Interest (SI) = $1095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1095
= $4745
Thus, Amount to be paid = $4745 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(2) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?