An investment of $800 was deposited to a bank semiannually for two years. The bank offered an interest rate of 8%, compounded continuously at the time of deposit. How much money will be in the account at the end of two years

The amount of money that will be in the account at the end of two years is $3,533.06.

Explanation:

Since the deposit will be made at the beginning of each period, the relevant formula to use is the formula for calculating the Future Value (FV) of an Annuity Due is employed as follows:

FV = M * {[(1 + r)^n - 1] ÷ r} * (1 + r) (1)

Where,

FV = Future value or the amount in the account after 2 years =?

M = Semiannual deposit = $800

r = Semiannual interest rate = 8% ÷ 2 = 4%, 0.04

n = Number of periods the deposit will be made = 2 years × 2 = 4

Substituting the values into equation (1), we have:

FV = $800 * {[(1 + 0.04)^4 - 1] ÷ 0.04} * (1 + 0.04)

FV = $800 * 4.246464 * 1.004

FV = $3,533.06

Therefore, the amount of money that will be in the account at the end of two years is $3,533.06.