Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
Correct Answer
$4828
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 7%
Time (t) = 6 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) = $3400 × 7% × 6
= $3400 ×7/100 × 6
= 3400 × 7 × 6/100
= 23800 × 6/100
= 142800/100
= $1428
Thus, Simple Interest = $1428
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 + $1428
= $4828
Thus, Amount to be paid = $4828 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 6)
= $3400 + ($3400 ×7/100 × 6)
= $3400 + (3400 × 7 × 6/100)
= $3400 + (23800 × 6/100)
= $3400 + (142800/100)
= $3400 + $1428 = $4828
Thus, Amount (A) to be paid = $4828 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 $3400, the simple interest in 1 year
= 7/100 × 3400
= 7 × 3400/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $238 × 6 = $1428
Thus, Simple Interest (SI) = $1428
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1428
= $4828
Thus, Amount to be paid = $4828 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(7) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(9) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(10) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.