Question

What lump sum should be deposited in an account that will earn 9% compounded every 2 months, to grow to $100,000 in 32 years? Show your step process, when you are solving the problem.

Answer 1

We should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.

Explanation:

To solve this problem, we can use the formula for compound interest:

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

where:

A = the future value of the investment

P = the initial principal (the lump sum we need to deposit)

r = the annual interest rate (9% in this case)

n = the number of times the interest is compounded per year (since interest is compounded every 2 months, or 6 times per year, n = 6)

t = the number of years (32 years in this case)

We are given that we want the investment to grow to $100,000 in 32 years, so we can set A = $100,000 and solve for P:

$100,000 = P(1 + 0.09/6)^(6*32)

Simplifying the expression inside the parentheses:

$100,000 = P(1.015)^192

Dividing both sides by (1.015)^192:

P = $100,000 / (1.015)^192

Using a calculator:

P ≈ $14,408.92

Therefore, we should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.