Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
Correct Answer
$7488
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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) = $5850 × 4% × 7
= $5850 ×4/100 × 7
= 5850 × 4 × 7/100
= 23400 × 7/100
= 163800/100
= $1638
Thus, Simple Interest = $1638
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 = $5850 + $1638
= $7488
Thus, Amount to be paid = $7488 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 = $5850
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 4% × 7)
= $5850 + ($5850 ×4/100 × 7)
= $5850 + (5850 × 4 × 7/100)
= $5850 + (23400 × 7/100)
= $5850 + (163800/100)
= $5850 + $1638 = $7488
Thus, Amount (A) to be paid = $7488 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 $5850, the simple interest in 1 year
= 4/100 × 5850
= 4 × 5850/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $234 × 7 = $1638
Thus, Simple Interest (SI) = $1638
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1638
= $7488
Thus, Amount to be paid = $7488 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.