Question

A deposit of AMD 1,000,000 was placed in the bank with an annual interest rate of 10%, with compound interest calculation (that is, at the end of each year, the amount at the beginning of the year increases by 10%). a) After 1 year, the account will have AMD... b) After 2 years, the depositor will have earned AMD... c) After 3 years, the total amount in the account will be... d) After 4 years, the depositor will have...

Answer 1

To calculate the future value of a deposit with compound interest, you can use the formula:

\[A = P(1 + r)^n\]

Where:

A = the future amount (including the initial deposit)

P = the principal amount (initial deposit)

r = annual interest rate (in decimal form)

n = number of years

In this case:

P = AMD 1,000,000

r = 10% or 0.10 (expressed as a decimal)

n = number of years

a) After 1 year:

\[A_1 = 1,000,000(1 + 0.10)^1 = 1,000,000(1.10) = 1,100,000\]

So, after 1 year, the account will have AMD 1,100,000.

b) After 2 years:

\[A_2 = 1,000,000(1 + 0.10)^2 = 1,000,000(1.10)^2 = 1,000,000(1.21) = 1,210,000\]

The depositor will have earned \(1,210,000 - 1,000,000 = \) AMD 210,000 in interest after 2 years.

c) After 3 years:

\[A_3 = 1,000,000(1 + 0.10)^3 = 1,000,000(1.10)^3 = 1,000,000(1.331) = 1,331,000\]

The total amount in the account after 3 years will be AMD 1,331,000.

d) After 4 years:

\[A_4 = 1,000,000(1 + 0.10)^4 = 1,000,000(1.10)^4 = 1,000,000(1.4641) = 1,464,100\]

The depositor will have earned \(1,464,100 - 1,000,000 = \) AMD 464,100 in interest after 4 years.

Explanation: