Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $10212

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 = $10212 – $6900 = $3312

Thus, Simple Interest = $3312

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 × 3312}/_{6900 × 6}

= ³³¹²⁰⁰/₄₁₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6900

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

Simple Interest = $3312 (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 $6900

= ⁶/₁₀₀ × 6900

= ^{6 × 6900}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $3312, then the time = ¹/₄₁₄ × 3312 years

= ^{1 × 3312}/₄₁₄ years

= ³³¹²/₄₁₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(2) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(7) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?