Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $7498

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 = $7498 – $4600 = $2898

Thus, Simple Interest = $2898

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 × 2898}/_{4600 × 7}

= ²⁸⁹⁸⁰⁰/₃₂₂₀₀

= 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) = $4600

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

Simple Interest = $2898 (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 $4600

= ⁷/₁₀₀ × 4600

= ^{7 × 4600}/₁₀₀

= ³²²⁰⁰/₁₀₀ = 322

Thus, simple Interest for 1 year = $322

Now,

∵ If the simple Interest is $322, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₂ years

∴ If the simple Interest is $2898, then the time = ¹/₃₂₂ × 2898 years

= ^{1 × 2898}/₃₂₂ years

= ²⁸⁹⁸/₃₂₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(3) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

(6) 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?

(7) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?