Question

Do you plan to retire in 35 years and you would like to have $1,00,000 in investments how much money would you have to invest today at 87% interest rate compounded daily to reach your goal in 35 years assume all years have 365 days round to the nearest cent

Answer 1

The man would have to invest $0.000000065 at an 87% interest rate to have $100000 after 35 years

To the nearest cent, it would be $0.00

Explanation:

Given information

The time for the investment = 35 years

The interest rate = 87%

The compounding period = 365

Total amount after the investment = $1,000, 000

Let the initial amount be P

To calculate the initial amount before the investment, we will need to apply the below formula

`A\text{ = P( 1 + }(r)/(n))^{n\cdot\text{ t}}`

Where

A = final amount

P = initial amount

r = rate

t = time

n = compounding period

The next step is to convert 87% to decimal

`\begin{gathered} 87\text{ \% = }(87)/(100) \\ 87\text{ \% = 0.87} \end{gathered}`

The next step is to substitute the given data into the compound interest formula

`\begin{gathered} 1000000\text{ = P (1 + }(0.87)/(365))^{365\cdot\text{ 35}} \\ 1000000=P(1+0.00238)^(12775) \\ 1000000=P(1.00238)^(12775) \\ 1000000\text{ = P (15446073591039)} \\ \text{Divide both sides by 15446073591039} \\ (1000000)/(15446073591039)\text{ = P} \\ P\text{ = \$ 0.0000000647} \end{gathered}`

Therefore, the man would have to invest $0.000000065 at an 87% interest rate to have $100000 after 35 years