How much do you need to invest today in order to have $1,000,000 in 30 years, at 5% annual interest, compounded daily?

Question

Answer the question by completing each box below.

Box 1 - Information

Box 2 - Find

Box 3 - Formula

Box 4 - Plug & Chug

Box 5 - Units

Answer 1

The underlying formula that you want to use here for compound interest is

P = A / (1 + r/n)^(nt)

Plugging in the values that we know that becomes

P = 1000000 / (1 + 0.05/365)^(365*30)

P = 1000000 / 4.481689

P = 223,153.08

meaning that the principal amount required to meet the criteria here is approximately $223,153.08

Answer 2

We know desired outcome, interest rate compounded daily, and duration of the investment.

We need to find the amount of the initial investment.

We will use the formula:

FV = PV x (1 + r/n)^(n x t)

Where:

FV = Future Value = $1,000,0000

PV = Present Value (the amount you need to invest today) = unknown

r = Annual interest rate = 5%

n = Number of times interest is compounded per year = 365 (daily)

t = Time (in years) = 30 years

Solving for PV, we get:

PV = $1,000,000 / (1 + 0.05/365)^(365 x 30) = $231,362.78

units are in $

Answer 3

PV = FV/(1 + r/n)^nt; PV = 1000000/(1 + 0.05/365)¹⁰⁹⁵⁰= $223153.08