Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
Correct Answer
$9282
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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) = $5950 × 7% × 8
= $5950 ×7/100 × 8
= 5950 × 7 × 8/100
= 41650 × 8/100
= 333200/100
= $3332
Thus, Simple Interest = $3332
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 + $3332
= $9282
Thus, Amount to be paid = $9282 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 8)
= $5950 + ($5950 ×7/100 × 8)
= $5950 + (5950 × 7 × 8/100)
= $5950 + (41650 × 8/100)
= $5950 + (333200/100)
= $5950 + $3332 = $9282
Thus, Amount (A) to be paid = $9282 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 $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416.5 × 8 = $3332
Thus, Simple Interest (SI) = $3332
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3332
= $9282
Thus, Amount to be paid = $9282 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(3) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(8) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?