Question

Suppose your bank compounds interest semi-annually (twice a year). How much will your current balance of $1,346 will become in 10 years if the bank gives an annual rate of return of 10%? (Round up your answer to two decimal point)

Answer 1

Using the compound interest formula for semi-annual compounding, the initial balance of $1,346 will become approximately $3,573.41 after 10 years with a 10% annual interest rate.

Step-by-step explanation:

To calculate the future balance of an account with compound interest semi-annually, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.

In this case, the initial balance (P) is $1,346, the annual interest rate (r) is 10% or 0.10, and the interest is compounded semi-annually, which means n = 2. The time period (t) is 10 years. Plugging these values into the formula gives us:

A = $1,346(1 + 0.10/2)2*10

A = $1,346(1 + 0.05)20

A = $1,346(1.05)20

A = $1,346 * 2.653297705

A ≈ $3,573.41

Therefore, after 10 years, the balance would become approximately $3,573.41 when rounded up to two decimal points.