Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7520

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 = $7520 – $4700 = $2820

Thus, Simple Interest = $2820

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 × 2820}/_{4700 × 10}

= ²⁸²⁰⁰⁰/₄₇₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4700

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

Simple Interest = $2820 (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 $4700

= ¹⁰/₁₀₀ × 4700

= ^{10 × 4700}/₁₀₀

= ⁴⁷⁰⁰⁰/₁₀₀ = 470

Thus, simple Interest for 1 year = $470

Now,

∵ If the simple Interest is $470, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₀ years

∴ If the simple Interest is $2820, then the time = ¹/₄₇₀ × 2820 years

= ^{1 × 2820}/₄₇₀ years

= ²⁸²⁰/₄₇₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(5) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?