Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
Correct Answer
$10735
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5650 × 10% × 9
= $5650 ×10/100 × 9
= 5650 × 10 × 9/100
= 56500 × 9/100
= 508500/100
= $5085
Thus, Simple Interest = $5085
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 = $5650 + $5085
= $10735
Thus, Amount to be paid = $10735 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 = $5650
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 9)
= $5650 + ($5650 ×10/100 × 9)
= $5650 + (5650 × 10 × 9/100)
= $5650 + (56500 × 9/100)
= $5650 + (508500/100)
= $5650 + $5085 = $10735
Thus, Amount (A) to be paid = $10735 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5650, the simple interest in 1 year
= 10/100 × 5650
= 10 × 5650/100
= 56500/100 = $565
Thus, simple interest for 1 year = $565
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $565 × 9 = $5085
Thus, Simple Interest (SI) = $5085
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $5085
= $10735
Thus, Amount to be paid = $10735 Answer
Similar Questions
(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(9) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?