Question:
What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
Correct Answer
$4225
Solution And Explanation
Solution
Given,
Principal (P) = $3250
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) = $3250 × 5% × 6
= $3250 ×5/100 × 6
= 3250 × 5 × 6/100
= 16250 × 6/100
= 97500/100
= $975
Thus, Simple Interest = $975
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 = $3250 + $975
= $4225
Thus, Amount to be paid = $4225 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 = $3250
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3250 + ($3250 × 5% × 6)
= $3250 + ($3250 ×5/100 × 6)
= $3250 + (3250 × 5 × 6/100)
= $3250 + (16250 × 6/100)
= $3250 + (97500/100)
= $3250 + $975 = $4225
Thus, Amount (A) to be paid = $4225 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 $3250, the simple interest in 1 year
= 5/100 × 3250
= 5 × 3250/100
= 16250/100 = $162.5
Thus, simple interest for 1 year = $162.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $162.5 × 6 = $975
Thus, Simple Interest (SI) = $975
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3250 + $975
= $4225
Thus, Amount to be paid = $4225 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(2) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(5) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) 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.
(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.