At what interest rate compounded quarterly will ₱ 90000 amount to ₱ 100000 in 8 years

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Imagine you put $ 100 in a savings account with a yearly interest rate of 6 % .

After one year, you have 100 + 6 = $ 106 . After two years, if the interest is simple , you will have 106 + 6 = $ 112 (adding 6 % of the original principal amount each year.) But if it is compound interest , then in the second year you will earn 6 % of the new amount:

1.06 × $ 106 = $ 112.36

Yearly Compound Interest Formula

If you put P dollars in a savings account with an annual interest rate r , and the interest is compounded yearly, then the amount A you have after t years is given by the formula:

A = P ( 1 + r ) t

Example:

Suppose you invest $ 4000 at 7 % interest, compounded yearly. Find the amount you have after 5 years.

Here, P = 4000 , r = 0.07 , and t = 5 . Substituting the values in the formula, we get:

A = 4000 ( 1 + 0.07 ) 5 ≈ 4000 ( 1.40255 ) = 5610.2

Therefore, the amount after 5 years would be about $ 5610.20 .

General Compound Interest Formula

If interest is compounded more frequently than once a year, you get an even better deal. In this case you have to divide the interest rate by the number of periods of compounding.

If you invest P dollars at an annual interest rate r , compounded n times a year, then the amount A you have after t years is given by the formula:

A = P ( 1 + r n ) n t

Example:

Suppose you invest $ 1000 at 9 % interest, compounded monthly. Find the amount you have after 18 months.

Here P = 1000 , r = 0.09 , n = 12 , and t = 1.5 (since 18 months = one and a half years).

Substituting the values, we get:

A = 1000 ( 1 + 0.09 12 ) 12 ( 1.5 ) ≈ 1000 ( 1.143960 ) = 1143.960

Rounding to the nearest cent, you have $ 1143.96 .

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