Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3840

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 = $3840 – $3200 = $640

Thus, Simple Interest = $640

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 × 640}/_{3200 × 4}

= ⁶⁴⁰⁰⁰/₁₂₈₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = $3200

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

Simple Interest = $640 (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 $3200

= ⁴/₁₀₀ × 3200

= ^{4 × 3200}/₁₀₀

= ¹²⁸⁰⁰/₁₀₀ = 128

Thus, simple Interest for 1 year = $128

Now,

∵ If the simple Interest is $128, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₈ years

∴ If the simple Interest is $640, then the time = ¹/₁₂₈ × 640 years

= ^{1 × 640}/₁₂₈ years

= ⁶⁴⁰/₁₂₈ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(2) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(4) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

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