Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8600

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8600 – $4300 = $4300

Thus, Simple Interest = $4300

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4300}/_{4300 × 10}

= ⁴³⁰⁰⁰⁰/₄₃₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4300 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $4300

= ¹⁰/₁₀₀ × 4300

= ^{10 × 4300}/₁₀₀

= ⁴³⁰⁰⁰/₁₀₀ = 430

Thus, simple Interest for 1 year = $430

Now,

∵ If the simple Interest is $430, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₀ years

∴ If the simple Interest is $4300, then the time = ¹/₄₃₀ × 4300 years

= ^{1 × 4300}/₄₃₀ years

= ⁴³⁰⁰/₄₃₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(9) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.