Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
Correct Answer
$7684
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5650 × 4% × 9
= $5650 ×4/100 × 9
= 5650 × 4 × 9/100
= 22600 × 9/100
= 203400/100
= $2034
Thus, Simple Interest = $2034
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 = $5650 + $2034
= $7684
Thus, Amount to be paid = $7684 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 = $5650
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 4% × 9)
= $5650 + ($5650 ×4/100 × 9)
= $5650 + (5650 × 4 × 9/100)
= $5650 + (22600 × 9/100)
= $5650 + (203400/100)
= $5650 + $2034 = $7684
Thus, Amount (A) to be paid = $7684 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5650, the simple interest in 1 year
= 4/100 × 5650
= 4 × 5650/100
= 22600/100 = $226
Thus, simple interest for 1 year = $226
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $226 × 9 = $2034
Thus, Simple Interest (SI) = $2034
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2034
= $7684
Thus, Amount to be paid = $7684 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(2) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(4) 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.
(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(10) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.