Question

112. Dani has $1,000 in an investment account that earns 3% per year, compounded monthly.

d. Boris also has $1,000, but in an account that earns 3% per year, compounded yearly. Write an explicit formula for the amount of money in his account after t years.

Answer 1

The formula of Compound Interest is:

`A = P(1+(r)/(n))^(nt)`

where A = Amount

P = Principle

r = rate

n = Number of Compounding per year

t = total number of year

a. For Dani

Here, P = 1000, r = 3% = 0.03, n = 12(monthly), and time = t.

Putting all these values in above formula:

`A = 1000(1+(0.03)/(12))^(12*t)`

⇒
`A = 1000((12.03)/(12))^(12t)`

⇒
`A = 1000(1.0025)^(12t)`

b. For Boris

`A = 1000(1+(0.03)/(1))^(t)`

⇒
`A = 1000(1.03)^(t)`