Question:
What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
Correct Answer
$4970
Solution And Explanation
Solution
Given,
Principal (P) = $3500
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) = $3500 × 7% × 6
= $3500 ×7/100 × 6
= 3500 × 7 × 6/100
= 24500 × 6/100
= 147000/100
= $1470
Thus, Simple Interest = $1470
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 = $3500 + $1470
= $4970
Thus, Amount to be paid = $4970 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 = $3500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 6)
= $3500 + ($3500 ×7/100 × 6)
= $3500 + (3500 × 7 × 6/100)
= $3500 + (24500 × 6/100)
= $3500 + (147000/100)
= $3500 + $1470 = $4970
Thus, Amount (A) to be paid = $4970 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 $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $245 × 6 = $1470
Thus, Simple Interest (SI) = $1470
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1470
= $4970
Thus, Amount to be paid = $4970 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(3) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(4) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(6) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?