Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3622.5

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 = $3622.5 – $3150 = $472.5

Thus, Simple Interest = $472.5

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 × 472.5}/_{3150 × 3}

= ⁴⁷²⁵⁰/₉₄₅₀

= 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) = $3150

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

Simple Interest = $472.5 (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 $472.5, then the time = ¹/_94.5 × 472.5 years

= ^{1 × 472.5}/_94.5 years

= ^472.5/_94.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(5) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(7) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

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

(10) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.