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 $8930 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8930

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 = $8930 – $4700 = $4230

Thus, Simple Interest = $4230

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 × 4230}/_{4700 × 10}

= ⁴²³⁰⁰⁰/₄₇₀₀₀

= 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) = $4700

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

Simple Interest = $4230 (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 $4230, then the time = ¹/₄₇₀ × 4230 years

= ^{1 × 4230}/₄₇₀ years

= ⁴²³⁰/₄₇₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(2) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(6) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.