Question

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $1,600 payments and has an APR of 7.7 percent compounded monthly. Investment B is a 7.2 percent continuously compounded lump sum investment, also good for 12 years. How much money would you need to invest in Investment B today for it to be worth as much as Investment A 12 years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)01

Answer 1

To invest in Investment B to match the value of Investment A after 12 years, approximately $5,414.41 needs to be invested today.

Step-by-step explanation:

To find out how much money would need to be invested in Investment B today for it to be worth as much as Investment A 12 years from now, we need to calculate the future value of Investment A and the present value of Investment B.

For Investment A, we will use the formula for the future value of an annuity:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the regular payment, r is the interest rate per period, and n is the number of periods.

Substituting the given values into the formula, we get:

FV(A) = $1,600 * [(1 + 0.077/12)^(12*12) - 1] / (0.077/12)

For Investment B, we will use the formula for the present value of a continuously compounded lump sum:

PV = FV / exp(r * n)

Where PV is the present value, FV is the future value, r is the interest rate continuously compounded, and n is the number of periods.

Substituting the given values into the formula, we get:

PV(B) = FV(A) / exp(0.072 * 12)

Calculating these values, we find that the amount of money that needs to be invested in Investment B today is approximately $5,414.41.