Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6970

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 = $6970 – $4100 = $2870

Thus, Simple Interest = $2870

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 × 2870}/_{4100 × 10}

= ²⁸⁷⁰⁰⁰/₄₁₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4100

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

Simple Interest = $2870 (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 $4100

= ¹⁰/₁₀₀ × 4100

= ^{10 × 4100}/₁₀₀

= ⁴¹⁰⁰⁰/₁₀₀ = 410

Thus, simple Interest for 1 year = $410

Now,

∵ If the simple Interest is $410, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₀ years

∴ If the simple Interest is $2870, then the time = ¹/₄₁₀ × 2870 years

= ^{1 × 2870}/₄₁₀ years

= ²⁸⁷⁰/₄₁₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?

(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(8) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?