Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9943

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 = $9943 – $6100 = $3843

Thus, Simple Interest = $3843

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 × 3843}/_{6100 × 7}

= ³⁸⁴³⁰⁰/₄₂₇₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6100

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3843 (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 = 7% of Principal

= 7% of $6100

= ⁷/₁₀₀ × 6100

= ^{7 × 6100}/₁₀₀

= ⁴²⁷⁰⁰/₁₀₀ = 427

Thus, simple Interest for 1 year = $427

Now,

∵ If the simple Interest is $427, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₇ years

∴ If the simple Interest is $3843, then the time = ¹/₄₂₇ × 3843 years

= ^{1 × 3843}/₄₂₇ years

= ³⁸⁴³/₄₂₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(2) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(9) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.