Question

What is the future value of $1,100, placed in a saving account for four years if the account pays 6.00% compounded quarterly? (your answer should be correct to two decimal places.)

Answer 1

The future value of $1,100 compounded quarterly at 6% for four years is $1,395.06.

Step-by-step explanation:

The student asked what the future value of $1,100 placed in a savings account for four years would be if the account pays 6.00% interest compounded quarterly. To calculate the future value of an investment, we use the formula for compound interest:

FV = P × (1 + r/n)nt

Where:

FV is the future value of the investment,

P is the principal amount ($1,100),

r is the annual interest rate (6% or 0.06),

n is the number of times the interest is compounded per year (quarterly compounding means n = 4),

t is the number of years the money is invested (4 years).

So, the calculation would be:

FV = $1,100 × (1 + 0.06/4)4×4

First, divide the annual rate by the number of compounding periods per year:

0.06/4 = 0.015

Next, add 1 to that result:

1 + 0.015 = 1.015

Now, raise this result to the power of the number of compounding periods (n×t):

1.01516 = 1.26824 (rounded to 5 decimal places)

Multiply this by the principal amount:

FV = $1,100 × 1.26824

FV = $1,395.06

Therefore, the future value of $1,100 compounded quarterly at 6% for four years is $1,395.06.