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 $6880 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6880

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 = $6880 – $4300 = $2580

Thus, Simple Interest = $2580

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 × 2580}/_{4300 × 10}

= ²⁵⁸⁰⁰⁰/₄₃₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $2580 (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 $2580, then the time = ¹/₄₃₀ × 2580 years

= ^{1 × 2580}/₄₃₀ years

= ²⁵⁸⁰/₄₃₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.

(2) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(6) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(10) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.