Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
Correct Answer
$8330
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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% × 10
= $5950 ×4/100 × 10
= 5950 × 4 × 10/100
= 23800 × 10/100
= 238000/100
= $2380
Thus, Simple Interest = $2380
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 + $2380
= $8330
Thus, Amount to be paid = $8330 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) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 10)
= $5950 + ($5950 ×4/100 × 10)
= $5950 + (5950 × 4 × 10/100)
= $5950 + (23800 × 10/100)
= $5950 + (238000/100)
= $5950 + $2380 = $8330
Thus, Amount (A) to be paid = $8330 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 10 years
= Simple interest for 1 year × 10
= $238 × 10 = $2380
Thus, Simple Interest (SI) = $2380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2380
= $8330
Thus, Amount to be paid = $8330 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(2) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(7) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(8) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.