Question

What amount must be invested for 6 months at 3.3% compounded monthly to reach a maturity value of $12,100? (Round dollar values to two decimal places.)

N=
PV =
FV =
How much interest ($) is earned over the period?

Answer 1

To reach a maturity value of $12,100 in 6 months at a 3.3% interest rate compounded monthly, approximately $11,869.79 needs to be invested. The interest earned over the period is $230.21.

Step-by-step explanation:

To calculate the amount that must be invested for 6 months at 3.3% compounded monthly to reach a maturity value of $12,100, we can use the formula for compound interest:

FV = PV(1 + r/n)^(nt)

Where:

• FV = Future Value ($12,100 in this case)
• PV = Present Value (unknown)
• r = Interest rate (3.3% or 0.033 as a decimal)
• n = Number of compounding periods in a year (12 as it is compounded monthly)
• t = Number of years (6 months = 0.5 years)

Plugging the values into the formula:

$12,100 = PV(1 + 0.033/12)^(12*0.5)

Simplifying the equation:

PV = $12,100 / (1 + 0.033/12)^(12*0.5)

Using a calculator, the approximate value of PV is $11,869.79.

To calculate the interest earned over the period, we can subtract the principal (PV) from the future value (FV):

Interest = FV - PV = $12,100 - $11,869.79 = $230.21.