Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
Correct Answer
$4380
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3650 ×5/100 × 4
= 3650 × 5 × 4/100
= 18250 × 4/100
= 73000/100
= $730
Thus, Simple Interest = $730
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 + $730
= $4380
Thus, Amount to be paid = $4380 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) = 4 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 4)
= $3650 + ($3650 ×5/100 × 4)
= $3650 + (3650 × 5 × 4/100)
= $3650 + (18250 × 4/100)
= $3650 + (73000/100)
= $3650 + $730 = $4380
Thus, Amount (A) to be paid = $4380 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 4 years
= Simple interest for 1 year × 4
= $182.5 × 4 = $730
Thus, Simple Interest (SI) = $730
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $730
= $4380
Thus, Amount to be paid = $4380 Answer
Similar Questions
(1) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.