Question

In: Statistics and Probability

You invest $2600 in an account that pays an APR of 6%. (a) What is the...

You invest $2600 in an account that pays an APR of 6%.

(a) What is the value of the investment after three years if interest is compounded yearly? Round your answer to the nearest cent.

The value of the investment after three years is $  .


(b) What is the value of the investment after three years if interest is compounded monthly? Round your answer to the nearest cent.

The value of the investment after three years is $  .

Solutions

Expert Solution

SOLUTION:

From given data,

You invest $2600 in an account that pays an APR of 6%.

Compound interest formula is given by

A = P ( 1 + r / n)nt

where,

A -> Final amount

P -> Principal

r -> Rate of interest (decimal)

n -> Number of times interest is compounded per year

t -> Time in years

(a) What is the value of the investment after three years if interest is compounded yearly

A = P ( 1 + r / n)nt

Here

P = 2600

APR(Annual percentage rate ) is  6%.

That is  

r = 6% = 6/100 = 0.06

interest is compound yearly

Therefore  

n = 1

we have to find amount after 3 years, That is t = 3  

A = 2600 ( 1 + 0.06 / 1)1*3  

= 2600 * (1.06)3

= 3096.6416

1$ = 1 cent

That is , value of investment after 3 years is = $ 3096.6416

(b) What is the value of the investment after three years if interest is compounded monthly

A = P ( 1 + r / n)nt

Here

P = 2600

APR(Annual percentage rate ) is  6%.

That is  

r = 6% = 6/100 = 0.06

interest is compound monthly

1 year = 12 months

Therefore  

n = 12

we have to find amount after 3 years, That is t = 3  

A = 2600 ( 1 + 0.06 / 12)12*3  

= 2600 * (1.005)36

= 3111.37

1$ = 1 cent

That is , value of investment after 3 years is = $ 3111.37


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