Question

A principal of ​$6000 is invested in an account paying an annual rate of 5​%. Find the amount in the account after 4 years if the account is compounded​ semiannually, quarterly, and monthly. ​(a) The amount in the account after 4 years if the account is compounded semiannually is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

Solution :

Given :

Principal amount deposited, P = $ 6000

Rate of interest, r = 5%

Number of years, t = 4 years

When the deposited amount is compounded semiannually, i.e. n = 2

Therefore,

Future value,

$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$

$FV = 6000\left( 1 +\frac{0.05}{2}\right)^{2 \times 4}$

$FV = 6000 \times (1.025)^8$

       = 6000 x 1.2184

        = 7310.4

Therefore, after 4 years there will be $ 7310.4 in the amount when compounded semi annually.

When the deposited amount is compounded quarterly, i.e. n = 4

Therefore,

Future value,

$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$

$FV = 6000\left( 1 +\frac{0.05}{4}\right)^{4 \times 4}$

$FV = 6000 \times (1.0125)^{16}$

       = 6000 x 1.219889

        = 7319.334

Therefore, after 4 years there will be $ 7319.334 in the amount when compounded quarterly.

When the deposited amount is compounded monthly, i.e. n = 12

Therefore,

Future value,

$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$

$FV = 6000\left( 1 +\frac{0.05}{12}\right)^{12 \times 4}$

$FV = 6000 \times (1.0041667)^{48}$

       = 6000 x 1.22089

        = 7325.34

Therefore, after 4 years there will be $ 7325.34 in the amount when compounded monthly.