Question

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

a. Write a recursive sequence for the amount of money in her account after n months.

Answer 1

Vf = Vi*(1 + 0.00247n)

Explanation:

The interest rate can be converted from anual to monthly by the equation:

(1 + im)¹² = 1 + iy, where im is the interest rate per monthly and iy the interest rate per year:

(1 + im)¹² = 1 + 0.03

1+ im =
`1.03^(1/12)`

1+ im = 1.00247

im = 0.00247 = 0.247%

The final amount (Vf) can be calculated knowing the initial amount (Vi):

Vf = Vi*(1 + im*n), where n is the number of monthes:

Vf = Vi*(1 + 0.00247n)