Question

Your aunt just won the lottery and gave you a gift of $15,000 to invest!! You invest in an account that will earn 7.8%

compounded quarterly. How much money will be in the account after 6 yours? After 15 years?

Answer 1

Answer: after 6 years, the account will have approximately $23,394.27, and after 15 years, the account will have approximately $54,765.15.

Explanation:

FV = Future value

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Number of years

Given that you received $15,000 from your aunt and the interest rate is 7.8% compounded quarterly, we can calculate the future values as follows:

After 6 years:

P = $15,000

r = 7.8% or 0.078 (as a decimal)

n = 4 (quarterly compounding)

t = 6 years

FV = $15,000 * (1 + 0.078/4)^(4*6)

FV = $15,000 * (1 + 0.0195)^24

FV = $15,000 * (1.0195)^24

FV ≈ $15,000 * 1.559618

FV ≈ $23,394.27

After 15 years:

P = $15,000

r = 7.8% or 0.078 (as a decimal)

n = 4 (quarterly compounding)

t = 15 years

FV = $15,000 * (1 + 0.078/4)^(4*15)

FV = $15,000 * (1 + 0.0195)^60

FV ≈ $15,000 * (1.0195)^60

FV ≈ $15,000 * 3.651010

FV ≈ $54,765.15