Question

Simon invests $1,700 in an account that earns an annual interest rate of

4.5% compounded daily.
What is the value of Simon's investment after 4 years?

Answer 1

Using the compound interest formula, A = P(1 + r/n)^(nt), Simon's $1,700 investment at an annual interest rate of 4.5% compounded daily will be worth approximately $2,032.55 after 4 years.

Step-by-step explanation:

The value of Simon's investment after 4 years can be calculated using the compound interest formula, which is:

A = P(1 + r/n)nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for in years.

Given that Simon invests $1,700 at an annual interest rate of 4.5% compounded daily, we have:

A = $1,700(1 + 0.045/365)365 × 4

Now, we'll calculate the value of Simon's investment:

A = $1,700(1 + 0.00012328767)1460

Using a calculator:

A ≈ $1,700(1.195618153) ≈ $2,032.55

Thus, the value of Simon's investment after 4 years is approximately $2,032.55.

Answer 2

The formula for calculating the future value of an investment with interest compounded daily is:

FV = PV (1 + r/n)^(nt)

where:

FV = future value

PV = present value (initial investment)

r = annual interest rate (expressed as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, the annual interest rate is 4.5% (0.045), and the interest is compounded daily, so n = 365.

Substituting the given values into the formula, we get:

FV = 1700 (1 + 0.045/365)^(365*4)

Calculating this out we get:

FV = 1700 * (1+0.00012328767)^(1460)

FV = 1700 * (1.00012328767)^(1460)

FV = 1700 * 1.607538

FV = 2746.44

So the value of Simon's investment after 4 years is $2,746.44

It's worth noting that the interest rate is compounded daily, so the interest is being added to the account on a daily basis, that's why the final amount is higher than if it was compounded annually.

Step-by-step explanation: