Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

Correct Answer  $8470

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 6%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5500 × 6% × 9

= $5500 ×⁶/₁₀₀ × 9

= ^{5500 × 6 × 9}/₁₀₀

= ^{33000 × 9}/₁₀₀

= ²⁹⁷⁰⁰⁰/₁₀₀

= $2970

Thus, Simple Interest = $2970

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 = $5500 + $2970

= $8470

Thus, Amount to be paid = $8470 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 = $5500

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 6% × 9)

= $5500 + ($5500 ×⁶/₁₀₀ × 9)

= $5500 + (^{5500 × 6 × 9}/₁₀₀)

= $5500 + (^{33000 × 9}/₁₀₀)

= $5500 + (²⁹⁷⁰⁰⁰/₁₀₀)

= $5500 + $2970 = $8470

Thus, Amount (A) to be paid = $8470 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5500, the simple interest in 1 year

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = $330

Thus, simple interest for 1 year = $330

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $330 × 9 = $2970

Thus, Simple Interest (SI) = $2970

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2970

= $8470

Thus, Amount to be paid = $8470 Answer

Similar Questions

(1) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(8) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?

(10) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?