Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3507.5

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 = $3507.5 – $3050 = $457.5

Thus, Simple Interest = $457.5

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 × 457.5}/_{3050 × 5}

= ⁴⁵⁷⁵⁰/₁₅₂₅₀

= 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) = $3050

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $457.5 (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 = 5% of Principal

= 5% of $3050

= ⁵/₁₀₀ × 3050

= ^{5 × 3050}/₁₀₀

= ¹⁵²⁵⁰/₁₀₀ = 152.5

Thus, simple Interest for 1 year = $152.5

Now,

∵ If the simple Interest is $152.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_152.5 years

∴ If the simple Interest is $457.5, then the time = ¹/_152.5 × 457.5 years

= ^{1 × 457.5}/_152.5 years

= ^457.5/_152.5 = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?

(7) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(9) 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.

(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.