Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
Correct Answer
$6936
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5100 × 4% × 9
= $5100 ×4/100 × 9
= 5100 × 4 × 9/100
= 20400 × 9/100
= 183600/100
= $1836
Thus, Simple Interest = $1836
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 = $5100 + $1836
= $6936
Thus, Amount to be paid = $6936 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 = $5100
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 9)
= $5100 + ($5100 ×4/100 × 9)
= $5100 + (5100 × 4 × 9/100)
= $5100 + (20400 × 9/100)
= $5100 + (183600/100)
= $5100 + $1836 = $6936
Thus, Amount (A) to be paid = $6936 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $204 × 9 = $1836
Thus, Simple Interest (SI) = $1836
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1836
= $6936
Thus, Amount to be paid = $6936 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(3) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?