Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
Correct Answer
$5467
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3850 × 7% × 6
= $3850 ×7/100 × 6
= 3850 × 7 × 6/100
= 26950 × 6/100
= 161700/100
= $1617
Thus, Simple Interest = $1617
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 = $3850 + $1617
= $5467
Thus, Amount to be paid = $5467 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 = $3850
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 7% × 6)
= $3850 + ($3850 ×7/100 × 6)
= $3850 + (3850 × 7 × 6/100)
= $3850 + (26950 × 6/100)
= $3850 + (161700/100)
= $3850 + $1617 = $5467
Thus, Amount (A) to be paid = $5467 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3850, the simple interest in 1 year
= 7/100 × 3850
= 7 × 3850/100
= 26950/100 = $269.5
Thus, simple interest for 1 year = $269.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $269.5 × 6 = $1617
Thus, Simple Interest (SI) = $1617
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1617
= $5467
Thus, Amount to be paid = $5467 Answer
Similar Questions
(1) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(4) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(6) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(9) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?