Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7360

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 = $7360 – $4600 = $2760

Thus, Simple Interest = $2760

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 × 2760}/_{4600 × 10}

= ²⁷⁶⁰⁰⁰/₄₆₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4600

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $2760 (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 = 10% of Principal

= 10% of $4600

= ¹⁰/₁₀₀ × 4600

= ^{10 × 4600}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₀ years

∴ If the simple Interest is $2760, then the time = ¹/₄₆₀ × 2760 years

= ^{1 × 2760}/₄₆₀ years

= ²⁷⁶⁰/₄₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(7) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

(9) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?