Question:
What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
Correct Answer
$3648
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 7%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 2
= $3200 ×7/100 × 2
= 3200 × 7 × 2/100
= 22400 × 2/100
= 44800/100
= $448
Thus, Simple Interest = $448
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 + $448
= $3648
Thus, Amount to be paid = $3648 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) = 7%
And, Time (t) = 2 years
Thus, Amount (A)
= $3200 + ($3200 × 7% × 2)
= $3200 + ($3200 ×7/100 × 2)
= $3200 + (3200 × 7 × 2/100)
= $3200 + (22400 × 2/100)
= $3200 + (44800/100)
= $3200 + $448 = $3648
Thus, Amount (A) to be paid = $3648 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3200, the simple interest in 1 year
= 7/100 × 3200
= 7 × 3200/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $224 × 2 = $448
Thus, Simple Interest (SI) = $448
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $448
= $3648
Thus, Amount to be paid = $3648 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(6) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.