Question

If 49600 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. a) annual: b) semiannual: c) monthly: d) daily:

Answer 1

a) Value of invest when compounded annually= $72878.67

b) Value of invest when compounded semi-annually is $73420.12

c) Value of invest when compounded monthly is $73896.35

Step-by-step explanation

a)Annually

Given:

Principal(p)= 49600

rate (r) = 8% = 0.08

time(t) =5

Since it is compounded anually, n=1

Using the formula;

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

Substitute the value and evaluate.

`A=49600(1+(0.08)/(1))^5`
`=49600(1.08)^5`
`=72878.67`

Therefore, the value of the investment when compounded annually is $72878.67

b) Semi-annually

In this case, the we are going to substitute all our initial values except for n.

In the case of semi annually, n= 2

That is;

Principal(p)= 49600

rate (r) = 8% = 0.08

time(t) =5

n=2

Substitute into the formula and evaluate.

`A=49600(1+(0.08)/(2))^(2*5)`
`=49600(1+0.04)^(10)`

`=49600(1.04)^(10)`
`=73420.12`

Therefore, the value of the investment when compounded semi-annually is $73420.12

c)monthly

In this case n= 12 and all other values remains the same.

That is;

Principal(p)= 49600

rate (r) = 8% = 0.08

time(t) =5

n=12

Substitute the values into the formula and evaluate.

`A=49600(1+(0.08)/(12))^(12*5)`

`=49600(1+0.667)^(60)`

`=49600(1.0667)^(60)`

`=73896.35`

Therefore, the value of the investment when compounded monthly is $73896.35