Question

Use the compound interest formulas upper a equals upper p left parenthesis 1 plus startfraction r over n endfraction right parenthesis superscript nt and upper a equals pe superscript rt to solve the problem given. round answers to the nearest cent. find the accumulated value of an investment of $ 10 comma 000 for 3 years at an interest rate of 4.5 % if the money is

a. compounded​ semiannually;


b. compounded​ quarterly;


c. compounded monthly


d. compounded continuously.

Answer 1

a. A=$11,428.25

b. A=$11,436.74

c. A=$11,442.48

d. A=$14,445.37

Explanation:

The compound interest formula is:

`A=P(1+(r)/(n))^(nt)`

Where:

P=10,000

t= 3 years

r=0.045

n = periods compounded in a year.

a. compounded​ semiannually:

`A=10,000(1+(0.045)/(2))^(2*3)\\A=11,428.25`

b. compounded​ quarterly:

`A=10,000(1+(0.045)/(4))^(4*3)\\A=11,436.74`

c. compounded monthly:

`A=10,000(1+(0.045)/(12))^(12*3)\\A=11,442.48`

d. compounded continuously:

The continously compounded interest equation is:

`A=10,000e^((0.045*3))\\A=14,445.37`