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 $7526 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $7526

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 = $7526 – $5300 = $2226

Thus, Simple Interest = $2226

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 × 2226}/_{5300 × 7}

= ²²²⁶⁰⁰/₃₇₁₀₀

= 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) = $5300

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

Simple Interest = $2226 (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 $2226, then the time = ¹/₃₇₁ × 2226 years

= ^{1 × 2226}/₃₇₁ years

= ²²²⁶/₃₇₁ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.

(4) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.

(8) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.