Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
Correct Answer
$8092
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 4% × 9
= $5950 ×4/100 × 9
= 5950 × 4 × 9/100
= 23800 × 9/100
= 214200/100
= $2142
Thus, Simple Interest = $2142
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 + $2142
= $8092
Thus, Amount to be paid = $8092 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 9)
= $5950 + ($5950 ×4/100 × 9)
= $5950 + (5950 × 4 × 9/100)
= $5950 + (23800 × 9/100)
= $5950 + (214200/100)
= $5950 + $2142 = $8092
Thus, Amount (A) to be paid = $8092 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 9 years
= Simple interest for 1 year × 9
= $238 × 9 = $2142
Thus, Simple Interest (SI) = $2142
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2142
= $8092
Thus, Amount to be paid = $8092 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.