Question:
What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
Correct Answer
$3840
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 10%
Time (t) = 2 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) = $3200 × 10% × 2
= $3200 ×10/100 × 2
= 3200 × 10 × 2/100
= 32000 × 2/100
= 64000/100
= $640
Thus, Simple Interest = $640
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 = $3200 + $640
= $3840
Thus, Amount to be paid = $3840 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 = $3200
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 2 years
Thus, Amount (A)
= $3200 + ($3200 × 10% × 2)
= $3200 + ($3200 ×10/100 × 2)
= $3200 + (3200 × 10 × 2/100)
= $3200 + (32000 × 2/100)
= $3200 + (64000/100)
= $3200 + $640 = $3840
Thus, Amount (A) to be paid = $3840 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 $3200, the simple interest in 1 year
= 10/100 × 3200
= 10 × 3200/100
= 32000/100 = $320
Thus, simple interest for 1 year = $320
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $320 × 2 = $640
Thus, Simple Interest (SI) = $640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $640
= $3840
Thus, Amount to be paid = $3840 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.