Question

Meg invested $16,000 in a savings account. If the annual interest rate is 6%, how much will be in the account in 5 years for quarterly compounding?

Answer 1

To calculate the future value of a $16,000 investment with a quarterly compounding interest rate of 6% over 5 years, the compound interest formula is used, and the investment grows to $21,549.68.

Step-by-step explanation:

The question asks about the future value of an investment of $16,000 with a quarterly compounding interest rate of 6% over 5 years. To calculate this, 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 ($16,000),
• r is the annual interest rate (6% or 0.06),
• n is the number of times that interest is compounded per year (quarterly means 4 times per year),
• t is the time the money is invested for in years (5 years).

Plugging the values into the formula:

FV = 16000 (1 + 0.06/4)^(4*5)

Now, calculate the values inside the parentheses and the exponent:

FV = 16000 (1 + 0.015)^(20)

FV = 16000 (1.015)^20

Now calculate the power of 1.015 raised to 20:

FV = 16000 * 1.346855007

Now, multiply the principal amount by this factor:

FV = 21,549.68

Therefore, the amount in the savings account after 5 years with quarterly compounding will be $21,549.68.