For this problem, use the compound interest formulas A =P(1+ r/n)^nt and A =Pe^r
ID: 2859466 • Letter: F
Question
For this problem, use the compound interest formulas A =P(1+ r/n)^nt and A =Pe^rt to compute the value of each investment after 4 years. Show all work.
a) $2000 invested at 4.25% compounded monthly.
b) $2000 invested at 4.35% compounded quarterly.
c) $2000 invested at 4.2% compounded daily.
d) $2000 invested at 4.15% compounded continuously.
e) Based on the answers to parts a-d, what has a larger effect on the accumulated amount, the interest rate or the number of times the interest is compounded?
Explanation / Answer
a) $2000 invested at 4.25% compounded monthly.
p=2000, r=0.0425,n=12,t=4
A =2000(1+ (0.0425/12))^(12*4)
A =2370
b) $2000 invested at 4.35% compounded quarterly.
p=2000, r=0.0435,n=4,t=4
A =2000(1+ (0.0435/4))^(4*4)
A =2378
c) $2000 invested at 4.2% compounded daily.
p=2000, r=0.042,n=365,t=4
A =2000(1+ (0.042/365))^(365*4)
A =2366
d) $2000 invested at 4.15% compounded continuously.A =Pe^rt
A =2000e0.0415*4
A =2361
the number of times the interest is compounded has a larger effect on the accumulated amount
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