Simple Interest
MCQs Math

Question:     Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $8162

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 = $8162 – $5300 = $2862

Thus, Simple Interest = $2862

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 × 2862}/_{5300 × 6}

= ²⁸⁶²⁰⁰/₃₁₈₀₀

= 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) = 6% per annum

Simple Interest = $2862 (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 $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $2862, then the time = ¹/₃₁₈ × 2862 years

= ^{1 × 2862}/₃₁₈ years

= ²⁸⁶²/₃₁₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

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

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(7) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(10) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?