Simple Interest
Math MCQs

Question :    Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

Correct Answer  $4485

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 10%

Time (t) = 3 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3450 × 10% × 3

= $3450 ×¹⁰/₁₀₀ × 3

= ^{3450 × 10 × 3}/₁₀₀

= ^{34500 × 3}/₁₀₀

= ¹⁰³⁵⁰⁰/₁₀₀

= $1035

Thus, Simple Interest = $1035

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 = $3450 + $1035

= $4485

Thus, Amount to be paid = $4485 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 = $3450

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 3 years

Thus, Amount (A)

= $3450 + ($3450 × 10% × 3)

= $3450 + ($3450 ×¹⁰/₁₀₀ × 3)

= $3450 + (^{3450 × 10 × 3}/₁₀₀)

= $3450 + (^{34500 × 3}/₁₀₀)

= $3450 + (¹⁰³⁵⁰⁰/₁₀₀)

= $3450 + $1035 = $4485

Thus, Amount (A) to be paid = $4485 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $3450, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3450

= ^{10 × 3450}/₁₀₀

= ³⁴⁵⁰⁰/₁₀₀ = $345

Thus, simple interest for 1 year = $345

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $345 × 3 = $1035

Thus, Simple Interest (SI) = $1035

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $1035

= $4485

Thus, Amount to be paid = $4485 Answer

Similar Questions

(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(5) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.