Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $11560

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 = $11560 – $6800 = $4760

Thus, Simple Interest = $4760

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 × 4760}/_{6800 × 7}

= ⁴⁷⁶⁰⁰⁰/₄₇₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6800

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

Simple Interest = $4760 (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 $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $4760, then the time = ¹/₄₇₆ × 4760 years

= ^{1 × 4760}/₄₇₆ years

= ⁴⁷⁶⁰/₄₇₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(6) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

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

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(10) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.