24.8k views
5 votes
suppose you deposit $10,000 in an account today that pays an interest rate which is compounding monthly. if your goal is to have $2,000,000 in 40 years, the stated annual rate must be at least:

User Rikkit
by
7.5k points

1 Answer

7 votes

Answer:

We can use the formula for compound interest to solve this problem.

Formula: FV = PV*(1 + r/n)^(n*t)

Where:

FV = future value

PV = present value

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

In this problem, we are given:

PV = $10,000

FV = $2,000,000

t = 40 years

n = 12 (monthly compounding)

We need to find the minimum annual interest rate (r) required to reach the future value of $2,000,000.

We can rearrange the formula to solve for r:

r = n*((FV/PV)^(1/(n*t))) - n

Substituting the given values:

r = 12*((2,000,000/10,000)^(1/(12*40))) - 12

Simplifying:

r = 0.0874 or 8.74%

Therefore, the stated annual rate must be at least 8.74% to achieve a future value of $2,000,000 in 40 years with a $10,000 deposit and monthly compounding.

User Ravi Gupta
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories