23.You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 percent, how much will you have at the end of four years
That six percent is compounded
end of year 1
1.06 * 1400
end of year 2
1.06*1400 + 1.06^2*1400
end of year 3
1.06*1400 + 1.06^2*1400 + 1.06^3*1400
end of year 4
1.06*1400 + 1.06^2*1400 + 1.06^3*1400 +1.06^4*1400
= 1400 (1.06+1.06^2+1.06^3+1.06^4)
To find out how much you will have at the end of four years, you can use the future value formula for compound interest.
The formula for calculating the future value (FV) of an investment with compound interest is:
FV = P(1 + r/n)^(n*t)
Where:
FV = future value
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount is $1,400, the annual interest rate is 6% (or 0.06 in decimal form), and the investment is compounded annually, so n = 1. The time period is 4 years.
Using the formula, we can calculate the future value:
FV = 1400(1 + 0.06/1)^(1*4)
= 1400(1 + 0.06)^4
= 1400(1.06)^4
≈ 1400 * 1.262476
≈ 1765.46
Therefore, you will have approximately $1,765.46 at the end of four years.