You have a goal of having $100,000 five years from today.The return on the investment is expected to be 8% and will be compounded semiannually.The amount that needs to be invested today is closest to:

A) $67,556.
B) $56,420.
C) $71,195.
D) $35,034.

Question

khaled seder · Accepted Answer

Final Answer : A, Explanation :   To find the present value (the amount that needs to be invested today) to achieve a future value of $100,000 in 5 years with an 8% annual interest rate compounded semiannually, we use the formula for the present value of a single sum:   P V = F V ( 1 + r / n ) n t PV = \frac{FV}{(1 + r/n)^{nt}} P V = ( 1 + r / n ) n t F V ​  , where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. Plugging in the values:   PV = \frac{100,000}{(1 + 0.08/2)^{2*5}} = \frac{100,000}{(1 + 0.04)^{10}} ≈ $67,556  .

You have a goal of having $100,000 five years from today.The return on the investment is expected to be 8% and will be compounded semiannually.The amount that needs to be invested today is closest to:

A) $67,556.
B) $56,420.
C) $71,195.
D) $35,034.

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You have a goal of having $100,000 five years from today.The return on the investment is expected to be 8% and will be compounded semiannually.The amount that needs to be invested today is closest to:A) $67,556.B) $56,420.C) $71,195.D) $35,034.

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Learning Objectives

Learning Objectives

Related questions

You have a goal of having $100,000 five years from today.The return on the investment is expected to be 8% and will be compounded semiannually.The amount that needs to be invested today is closest to:

A) $67,556.
B) $56,420.
C) $71,195.
D) $35,034.