Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
Correct Answer
$7605
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5850 × 3% × 10
= $5850 ×3/100 × 10
= 5850 × 3 × 10/100
= 17550 × 10/100
= 175500/100
= $1755
Thus, Simple Interest = $1755
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 + $1755
= $7605
Thus, Amount to be paid = $7605 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 3% × 10)
= $5850 + ($5850 ×3/100 × 10)
= $5850 + (5850 × 3 × 10/100)
= $5850 + (17550 × 10/100)
= $5850 + (175500/100)
= $5850 + $1755 = $7605
Thus, Amount (A) to be paid = $7605 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 $5850, the simple interest in 1 year
= 3/100 × 5850
= 3 × 5850/100
= 17550/100 = $175.5
Thus, simple interest for 1 year = $175.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $175.5 × 10 = $1755
Thus, Simple Interest (SI) = $1755
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1755
= $7605
Thus, Amount to be paid = $7605 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(10) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?