Question

ASSUME that in 25 years you will need $500,000 for your retirement (i.e. retirement is actually 25 years away, and you want to have saved $500,000). How much money would you have to put into a bank today to accumulate this if your money will earn 8% per year (assume annual compounding)?
a.73,009

b.166,365

c.211, 573

d.676,001

e.insufficient information to compute

Answer 1

Answer:

The correct answer is:

$73,009 (a.)

Explanation:

Future value is the accumulated compounded interest on a certain amount (present value) invested over a specified period of time.

To calculate the future value or present value, the nominal annual interest, the duration of investment and the present value or future value respectively must be known. The relationship is shown mathematically as:

$FV=PV(1 + i)^{n}$

or $PV = \frac{FV}{(1 + i)^n}$

where FV = Future value

PV = present value

i = nominal interest rate in percentage

n = number of compounding period

note: nominal interest rate is interest rate before inflation adjustments or interest rate before the effect of compounding

In this question, we are to determine the present value (PV), because the future value after 25 years is set as $500,000.

∴ $PV = \frac{FV}{(1 + i)^n}$

$\\ PV = \frac{500,000}{(1 + 0.08)^2^5} = \frac{500,000}{6.8485} = 73,008.7$

= $73,009 (to the nearest dollars)