Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
Correct Answer
$7854
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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) = $5950 × 4% × 8
= $5950 ×4/100 × 8
= 5950 × 4 × 8/100
= 23800 × 8/100
= 190400/100
= $1904
Thus, Simple Interest = $1904
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 + $1904
= $7854
Thus, Amount to be paid = $7854 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 8)
= $5950 + ($5950 ×4/100 × 8)
= $5950 + (5950 × 4 × 8/100)
= $5950 + (23800 × 8/100)
= $5950 + (190400/100)
= $5950 + $1904 = $7854
Thus, Amount (A) to be paid = $7854 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 $5950, the simple interest in 1 year
= 4/100 × 5950
= 4 × 5950/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $238 × 8 = $1904
Thus, Simple Interest (SI) = $1904
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1904
= $7854
Thus, Amount to be paid = $7854 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(9) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.