Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8639

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 = $8639 – $5300 = $3339

Thus, Simple Interest = $3339

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 × 3339}/_{5300 × 7}

= ³³³⁹⁰⁰/₃₇₁₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5300

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3339 (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 = 7% of Principal

= 7% of $5300

= ⁷/₁₀₀ × 5300

= ^{7 × 5300}/₁₀₀

= ³⁷¹⁰⁰/₁₀₀ = 371

Thus, simple Interest for 1 year = $371

Now,

∵ If the simple Interest is $371, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₁ years

∴ If the simple Interest is $3339, then the time = ¹/₃₇₁ × 3339 years

= ^{1 × 3339}/₃₇₁ years

= ³³³⁹/₃₇₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

(2) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.

(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.