In: Statistics and Probability
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 $ .
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