Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3348

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 = $3348 – $3100 = $248

Thus, Simple Interest = $248

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 × 248}/_{3100 × 4}

= ²⁴⁸⁰⁰/₁₂₄₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = $3100

Rate of Simple Interest (R) = 4% per annum

Simple Interest = $248 (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 = 4% of Principal

= 4% of $3100

= ⁴/₁₀₀ × 3100

= ^{4 × 3100}/₁₀₀

= ¹²⁴⁰⁰/₁₀₀ = 124

Thus, simple Interest for 1 year = $124

Now,

∵ If the simple Interest is $124, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₄ years

∴ If the simple Interest is $248, then the time = ¹/₁₂₄ × 248 years

= ^{1 × 248}/₁₂₄ years

= ²⁴⁸/₁₂₄ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(3) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.

(4) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.