Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
Correct Answer
$8627.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5950 × 5% × 9
= $5950 ×5/100 × 9
= 5950 × 5 × 9/100
= 29750 × 9/100
= 267750/100
= $2677.5
Thus, Simple Interest = $2677.5
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 = $5950 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 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 = $5950
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 9)
= $5950 + ($5950 ×5/100 × 9)
= $5950 + (5950 × 5 × 9/100)
= $5950 + (29750 × 9/100)
= $5950 + (267750/100)
= $5950 + $2677.5 = $8627.5
Thus, Amount (A) to be paid = $8627.5 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 $5950, the simple interest in 1 year
= 5/100 × 5950
= 5 × 5950/100
= 29750/100 = $297.5
Thus, simple interest for 1 year = $297.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $297.5 × 9 = $2677.5
Thus, Simple Interest (SI) = $2677.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(2) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(5) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.