Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
Correct Answer
$4420
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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) = $3400 × 5% × 6
= $3400 ×5/100 × 6
= 3400 × 5 × 6/100
= 17000 × 6/100
= 102000/100
= $1020
Thus, Simple Interest = $1020
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 = $3400 + $1020
= $4420
Thus, Amount to be paid = $4420 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 = $3400
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 6)
= $3400 + ($3400 ×5/100 × 6)
= $3400 + (3400 × 5 × 6/100)
= $3400 + (17000 × 6/100)
= $3400 + (102000/100)
= $3400 + $1020 = $4420
Thus, Amount (A) to be paid = $4420 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 $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $170 × 6 = $1020
Thus, Simple Interest (SI) = $1020
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1020
= $4420
Thus, Amount to be paid = $4420 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.