Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
Correct Answer
$5070
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3900 × 5% × 6
= $3900 ×5/100 × 6
= 3900 × 5 × 6/100
= 19500 × 6/100
= 117000/100
= $1170
Thus, Simple Interest = $1170
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 = $3900 + $1170
= $5070
Thus, Amount to be paid = $5070 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 = $3900
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 5% × 6)
= $3900 + ($3900 ×5/100 × 6)
= $3900 + (3900 × 5 × 6/100)
= $3900 + (19500 × 6/100)
= $3900 + (117000/100)
= $3900 + $1170 = $5070
Thus, Amount (A) to be paid = $5070 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3900, the simple interest in 1 year
= 5/100 × 3900
= 5 × 3900/100
= 19500/100 = $195
Thus, simple interest for 1 year = $195
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $195 × 6 = $1170
Thus, Simple Interest (SI) = $1170
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1170
= $5070
Thus, Amount to be paid = $5070 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(10) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.