Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
Correct Answer
$8282
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5050 × 8% × 8
= $5050 ×8/100 × 8
= 5050 × 8 × 8/100
= 40400 × 8/100
= 323200/100
= $3232
Thus, Simple Interest = $3232
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 = $5050 + $3232
= $8282
Thus, Amount to be paid = $8282 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 = $5050
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 8% × 8)
= $5050 + ($5050 ×8/100 × 8)
= $5050 + (5050 × 8 × 8/100)
= $5050 + (40400 × 8/100)
= $5050 + (323200/100)
= $5050 + $3232 = $8282
Thus, Amount (A) to be paid = $8282 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5050, the simple interest in 1 year
= 8/100 × 5050
= 8 × 5050/100
= 40400/100 = $404
Thus, simple interest for 1 year = $404
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $404 × 8 = $3232
Thus, Simple Interest (SI) = $3232
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3232
= $8282
Thus, Amount to be paid = $8282 Answer
Similar Questions
(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(5) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?