Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
Correct Answer
$7556.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5950 ×3/100 × 9
= 5950 × 3 × 9/100
= 17850 × 9/100
= 160650/100
= $1606.5
Thus, Simple Interest = $1606.5
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 + $1606.5
= $7556.5
Thus, Amount to be paid = $7556.5 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 3% × 9)
= $5950 + ($5950 ×3/100 × 9)
= $5950 + (5950 × 3 × 9/100)
= $5950 + (17850 × 9/100)
= $5950 + (160650/100)
= $5950 + $1606.5 = $7556.5
Thus, Amount (A) to be paid = $7556.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5950, the simple interest in 1 year
= 3/100 × 5950
= 3 × 5950/100
= 17850/100 = $178.5
Thus, simple interest for 1 year = $178.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $178.5 × 9 = $1606.5
Thus, Simple Interest (SI) = $1606.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1606.5
= $7556.5
Thus, Amount to be paid = $7556.5 Answer
Similar Questions
(1) 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.
(2) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?