At what rate percent per annum will a sum of PHP 2000 amount to PHP 2205 in 2 years compounded annually?

More solved problems on compound interest using formula are shown below.

1. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

Solution:

Given, SI = $ 6750, R = \(\frac{20}{3}\)% p.a. and T = 3 years.

sum = 100 × SI / R × T

= $ (100 × 6750 × ³/₂₀ × 1/3 ) = $ 33750.

Now, P = $ 33750, R = \(\frac{20}{3}\)% p.a. and T = 3 years. 

Therefore, amount after 3 years 

= $ {33750 × (1 + (20/3 × 100)}³ [using A = P (1 + R/100)ᵀ]

= $ (33750 × 16/15 × 16/15 × 16/15) = $ 40960.

Thus, amount = $ 40960.

Hence, compound interest = $ (40960 - 33750) = $ 7210.

2. The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.

Solution:

Let the sum be $ 100. Then,

SI = $ (100 × 6 × 2/100) = $ 12

and compound interest = $ {100 × (1 + 6/100)² - 100}

= $ {(100 × 53/50 × 53/50) - 100} = $ (2809/25 - 100) = $ 309/25

Therefore, (CI) - (SI) = $ (309/25 – 100) = $ 9/25

If the difference between the CI and SI is $ 9/25, then the sum = $ 100.

If the difference between the CI and SI is $ 18, then the sum = $ (100 × 25/9 × 18 )

= $ 5000.

Hence, the required sum is $ 5000.

Alternative method

Let the sum be $ P.

Then, SI = $ (P × 6/100 × 2) = $ 3P/25

And, CI = $ {P × (1 + 6/100)² - P}

= $ {(P × 53/50 × 53/50) - P} = $ (\(\frac{2809}{2500}\)P - P) = $ (309P/2500)

(CI) - (SI) = $ (309P/2500 – 3P/25) = $ (9P/2500)

Therefore, 9P/2500 = 18

⇔ P = 2500 × 18/9

⇔ P = 5000.

Hence, the required sum is $ 5000.

3. A certain sum amounts to $ 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.

Solution:

Let the sum be $ 100. Then,

amount = $ {100 × (1 + 8/100)²}

= $ (100 × 27/25 × 27/25) = $ (2916/25)

If the amount is $ 2916/25 then the sum = $ 100.

If the amount is $ 72900 then the sum = $ (100 × 25/2916 × 72900) = $ 62500.

Hence, the required sum is $ 62500.

Alternative method

Let the sum be $ P. Then,

amount = $ {P × (1 + 8/100)²}

= $ {P × 27/25 × 27/25} = $ (729P/625)

Therefore, 729P/625 = 72900

⇔ P = (72900 × 625)/729

⇔ P = 62500.

Hence, the required sum is $ 62500.

4. In this question the formula is when the interest is compounded annually to solve this problem on compound interest. 4. At what rate per cent per annum will Ron lends a sum of $2000 to Ben. Ben returned after 2 years $2205, compounded annually?

Solution:

Let the required rate be R% per annum.

Here, A = $ 2205, P = $ 2000 and n = 2 years.

Using the formula A = P(1 + R/100)ⁿ,

2205 = 2000 × ( 1 + R/100)²

⇒ (1 + R/100)² = 2205/2000 = 441/400 = (21/20)²

⇒ ( 1 + R/100) = 21/20

⇒ R/100 = (21/20 – 1) = 1/20

⇒ R = (100 × 1/20) = 5

Hence, the required rate of interest is 5% per annum.

5. A man deposited $1000 in a bank. In return he got $1331. Bank gave interest 10% per annum. How long did he kept the money in the bank?

Solution:

Let the required time be n years. Then,

amount = $ {1000 × (1 + 10/100)ⁿ}

= $ {1000 × (11/10)ⁿ}

Therefore, 1000 × (11/10)ⁿ = 1331 [since, amount = $ 1331 (given)]

⇒ (11/10)ⁿ = 1331/1000 = 11 × 11 × 11/ 10 × 10 × 10 = (11/10)³

⇒ (11/10)ⁿ = (11/10)³

⇒ n = 3.

Thus, n = 3.

Hence, the required time is 3 years.

● Compound Interest

Compound Interest

Compound Interest with Growing Principal

Compound Interest with Periodic Deductions

Compound Interest by Using Formula

Compound Interest when Interest is Compounded Yearly

Compound Interest when Interest is Compounded Half-Yearly

Compound Interest when Interest is Compounded Quarterly

Problems on Compound Interest

Variable Rate of Compound Interest

Difference of Compound Interest and Simple Interest

Practice Test on Compound Interest

Uniform Rate of Growth

Uniform Rate of Depreciation

Uniform Rate of Growth and Depreciation

● Compound Interest - Worksheet

Worksheet on Compound Interest

Worksheet on Compound Interest when Interest is Compounded Half-Yearly

Worksheet on Compound Interest with Growing Principal

Worksheet on Compound Interest with Periodic Deductions

Worksheet on Variable Rate of Compound Interest

Worksheet on Difference of Compound Interest and Simple Interest

Worksheet on Uniform Rate of Growth

Worksheet on Uniform Rate of Depreciation

Worksheet on Uniform Rate of Growth and Depreciation

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