Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
Correct Answer
$3717
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $3150 × 3% × 6
= $3150 ×3/100 × 6
= 3150 × 3 × 6/100
= 9450 × 6/100
= 56700/100
= $567
Thus, Simple Interest = $567
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 = $3150 + $567
= $3717
Thus, Amount to be paid = $3717 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 = $3150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 6)
= $3150 + ($3150 ×3/100 × 6)
= $3150 + (3150 × 3 × 6/100)
= $3150 + (9450 × 6/100)
= $3150 + (56700/100)
= $3150 + $567 = $3717
Thus, Amount (A) to be paid = $3717 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $94.5 × 6 = $567
Thus, Simple Interest (SI) = $567
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $567
= $3717
Thus, Amount to be paid = $3717 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(8) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?