Question

If you would like to accumulate $7,500 over the next 5 years, how much must you deposit each six months, starting six months from now, given a 6 percent interest rate and semiannual compounding?

Answer 1

To accumulate $7,500 over the next 5 years with a 6 percent interest rate and semiannual compounding, you would need to deposit $6,674.76 initially.

Step-by-step explanation:

To accumulate $7,500 over the next 5 years with a 6 percent interest rate and semiannual compounding, we can use the formula for compound interest:

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

Where:

• A is the future value
• P is the initial deposit
• r is the interest rate
• n is the number of times interest is compounded per year
• t is the number of years

Plugging in the given values:

A = $7,500, r = 6% or 0.06, n = 2 (semiannual compounding), t = 5 years

And solving for P:

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

Substituting the values:

P = $7,500 / (1 + 0.06/2)^(2 * 5)

P = $6,674.76