Shane wants to invest money in a 6% CD that compounds semiannually.Shane would like the account to have a balance of $100,000 four years from now.How much must Shane deposit to accomplish his goal?

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

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

where A is the end balance, P is the principal (initial deposit), r is the interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, A = $100,000, r = 0.06, n = 2 (since interest is compounded semiannually), and t = 4.

We can solve for P:

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

P = $100,000 / (1 + 0.06/2)^(2*4)

P = $78,940.86

Therefore, Shane must deposit $78,940.86 to have a balance of $100,000 after four years. The closest answer choice to this value is B, $78,941.

Shane Wants to Invest Money in a 6% CD That