Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7752

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 = $7752 – $5700 = $2052

Thus, Simple Interest = $2052

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 × 2052}/_{5700 × 6}

= ²⁰⁵²⁰⁰/₃₄₂₀₀

= 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) = $5700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2052 (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 = 6% of Principal

= 6% of $5700

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = 342

Thus, simple Interest for 1 year = $342

Now,

∵ If the simple Interest is $342, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₂ years

∴ If the simple Interest is $2052, then the time = ¹/₃₄₂ × 2052 years

= ^{1 × 2052}/₃₄₂ years

= ²⁰⁵²/₃₄₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(2) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.