Question

If $10,000 is invested at an annual rate of 11%, compounded quarterly, find the value of the investment after the given number of years.

a) 5 years b) 10 years c) 15 years

Answer 1

`a) A\simeq17204.28`

`b) A\simeq29598.74`

`c)A\simeq50922.51`

Explanation:

The amount formula in compound interest is:

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

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $10000

`r = 11\% = (11\%)/(100\%)=0.11`

n = 4 (quarterly in a year)

a ) t = 5 years

`A=10000(1+(0.11)/(4) )^((4)(5))\\\\A=10000(1+(0.11)/(4) )^(20)\\\\A=17204.28431\\\\A\simeq17204.28`

b) t = 10 years

`A=10000(1+(0.11)/(4) )^((4)(10))\\\\A=10000(1+(0.11)/(4) )^(40)\\\\A=29598.73987\\\\A\simeq29598.74`

c) t = 15 years

`A=10000(1+(0.11)/(4) )^((4)(15))\\\\A=10000(1+(0.11)/(4) )^(60)\\\\A=50922.51361\\\\A\simeq50922.51`

Answer 2

Solution given;

principal [p]=$10000

rate[r]=11%

time[t]= 5 years

we have

compound amount quarterly =P(1+r/400)^4t

=$10000(1+11/400)^4×5=$17204.28431