Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3433.5

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 = $3433.5 – $3150 = $283.5

Thus, Simple Interest = $283.5

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 × 283.5}/_{3150 × 3}

= ²⁸³⁵⁰/₉₄₅₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3150

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $283.5 (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 = 3% of Principal

= 3% of $3150

= ³/₁₀₀ × 3150

= ^{3 × 3150}/₁₀₀

= ⁹⁴⁵⁰/₁₀₀ = 94.5

Thus, simple Interest for 1 year = $94.5

Now,

∵ If the simple Interest is $94.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_94.5 years

∴ If the simple Interest is $283.5, then the time = ¹/_94.5 × 283.5 years

= ^{1 × 283.5}/_94.5 years

= ^283.5/_94.5 = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?

(5) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(9) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

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