Simple Interest
Math MCQs

Question :    In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3937.5

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 = $3937.5 – $3150 = $787.5

Thus, Simple Interest = $787.5

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 × 787.5}/_{3150 × 5}

= ⁷⁸⁷⁵⁰/₁₅₇₅₀

= 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) = 5% per annum

Simple Interest = $787.5 (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 $3150

= ⁵/₁₀₀ × 3150

= ^{5 × 3150}/₁₀₀

= ¹⁵⁷⁵⁰/₁₀₀ = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_157.5 years

∴ If the simple Interest is $787.5, then the time = ¹/_157.5 × 787.5 years

= ^{1 × 787.5}/_157.5 years

= ^787.5/_157.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?

(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

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

(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(9) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.