Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
Correct Answer
$7410
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5700 × 3% × 10
= $5700 ×3/100 × 10
= 5700 × 3 × 10/100
= 17100 × 10/100
= 171000/100
= $1710
Thus, Simple Interest = $1710
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 = $5700 + $1710
= $7410
Thus, Amount to be paid = $7410 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 = $5700
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 10)
= $5700 + ($5700 ×3/100 × 10)
= $5700 + (5700 × 3 × 10/100)
= $5700 + (17100 × 10/100)
= $5700 + (171000/100)
= $5700 + $1710 = $7410
Thus, Amount (A) to be paid = $7410 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 $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $171 × 10 = $1710
Thus, Simple Interest (SI) = $1710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1710
= $7410
Thus, Amount to be paid = $7410 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(4) Jennifer had to pay $3737.5 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 after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(6) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?