Question:
What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
Correct Answer
$5925
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3950 × 10% × 5
= $3950 ×10/100 × 5
= 3950 × 10 × 5/100
= 39500 × 5/100
= 197500/100
= $1975
Thus, Simple Interest = $1975
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 = $3950 + $1975
= $5925
Thus, Amount to be paid = $5925 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 = $3950
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3950 + ($3950 × 10% × 5)
= $3950 + ($3950 ×10/100 × 5)
= $3950 + (3950 × 10 × 5/100)
= $3950 + (39500 × 5/100)
= $3950 + (197500/100)
= $3950 + $1975 = $5925
Thus, Amount (A) to be paid = $5925 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3950, the simple interest in 1 year
= 10/100 × 3950
= 10 × 3950/100
= 39500/100 = $395
Thus, simple interest for 1 year = $395
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $395 × 5 = $1975
Thus, Simple Interest (SI) = $1975
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1975
= $5925
Thus, Amount to be paid = $5925 Answer
Similar Questions
(1) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.