Asked by Allyssa
Find the future value of an ordinary annuity that calls for depositing $100 at the end of every 6 months for 15 years into an account that earns 7% interest compounded semiannually. (Round your answer to the nearest cent.)
Answers
Answered by
MathMate
The future value FV can be calculated by summing payments and simplification using factorization:
FV = S(1+(1+r)+(1+r)^2+...+(1+r)r^(n-1))
=S((1+r)^n-1)/((1+r)-1)
=S((1+r)^n-1)/r
FV=future value
S=Semi-annual payment
r=interest per period (6-months)
n=number of periods (6-months)
Here you have
n=15*2=30
r=7%/2 = 0.035
S=$100
FV = S(1+(1+r)+(1+r)^2+...+(1+r)r^(n-1))
=S((1+r)^n-1)/((1+r)-1)
=S((1+r)^n-1)/r
FV=future value
S=Semi-annual payment
r=interest per period (6-months)
n=number of periods (6-months)
Here you have
n=15*2=30
r=7%/2 = 0.035
S=$100
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