Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8140

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 = $8140 – $5500 = $2640

Thus, Simple Interest = $2640

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 × 2640}/_{5500 × 6}

= ²⁶⁴⁰⁰⁰/₃₃₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 6% per annum

Simple Interest = $2640 (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 = 6% of Principal

= 6% of $5500

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = 330

Thus, simple Interest for 1 year = $330

Now,

∵ If the simple Interest is $330, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₀ years

∴ If the simple Interest is $2640, then the time = ¹/₃₃₀ × 2640 years

= ^{1 × 2640}/₃₃₀ years

= ²⁶⁴⁰/₃₃₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(7) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(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) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?