Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8112

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 = $8112 – $5200 = $2912

Thus, Simple Interest = $2912

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 × 2912}/_{5200 × 8}

= ²⁹¹²⁰⁰/₄₁₆₀₀

= 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) = $5200

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2912 (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 = 8% of Principal

= 8% of $5200

= ⁸/₁₀₀ × 5200

= ^{8 × 5200}/₁₀₀

= ⁴¹⁶⁰⁰/₁₀₀ = 416

Thus, simple Interest for 1 year = $416

Now,

∵ If the simple Interest is $416, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₆ years

∴ If the simple Interest is $2912, then the time = ¹/₄₁₆ × 2912 years

= ^{1 × 2912}/₄₁₆ years

= ²⁹¹²/₄₁₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?

(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(5) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

(9) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.