Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9120

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 = $9120 – $4800 = $4320

Thus, Simple Interest = $4320

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 × 4320}/_{4800 × 10}

= ⁴³²⁰⁰⁰/₄₈₀₀₀

= 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) = $4800

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4320 (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 = 10% of Principal

= 10% of $4800

= ¹⁰/₁₀₀ × 4800

= ^{10 × 4800}/₁₀₀

= ⁴⁸⁰⁰⁰/₁₀₀ = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₀ years

∴ If the simple Interest is $4320, then the time = ¹/₄₈₀ × 4320 years

= ^{1 × 4320}/₄₈₀ years

= ⁴³²⁰/₄₈₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(2) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(8) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(10) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.