Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 2% 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 × 2}

= ²⁴⁸⁰⁰/₆₂₀₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = 2% 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 = 2% of Principal

= 2% of $3100

= ²/₁₀₀ × 3100

= ^{2 × 3100}/₁₀₀

= ⁶²⁰⁰/₁₀₀ = 62

Thus, simple Interest for 1 year = $62

Now,

∵ If the simple Interest is $62, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂ years

∴ If the simple Interest is $248, then the time = ¹/₆₂ × 248 years

= ^{1 × 248}/₆₂ years

= ²⁴⁸/₆₂ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(6) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?

(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.

(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.