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) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(2) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(6) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.