Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9460

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 = $9460 – $5500 = $3960

Thus, Simple Interest = $3960

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 × 3960}/_{5500 × 8}

= ³⁹⁶⁰⁰⁰/₄₄₀₀₀

= 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) = $5500

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3960 (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 = 8% of Principal

= 8% of $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $3960, then the time = ¹/₄₄₀ × 3960 years

= ^{1 × 3960}/₄₄₀ years

= ³⁹⁶⁰/₄₄₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(8) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.