Question

Find the accumulated amount after 4 years if $1000 is invested at 6% per year compounded (a) daily (assume a 365-day year) and (b) continuously...Find the accumulated amount after 4 years if $1000 is invested at 6% per year compounded (a) annually, (b) semiannually, (c) quarterly, (d) monthly, and (e) daily.

Answer 1

1.

(a) Compound interest

$$A=P(1+\dfrac{r}{n})^{nt}$$

Daily: $n=365$

$$A=1000(1+\dfrac{0.06}{365})^{365(4)}=\$1271.22$$

(b) Continuously Compounded Interest

$$A=Pe^{rt}=1000e^{0.06(4)}=\$1271.25$$

2.

Compound interest

$$A=P(1+\dfrac{r}{n})^{nt}$$

(a) Annually $n=1$

$$A=1000(1+\dfrac{0.06}{1})^{1(4)}=\$1262.48$$

(b) Semiannually $n=2$

$$A=1000(1+\dfrac{0.06}{2})^{2(4)}=\$1266.77$$

(c) Quarterly $n=4$

$$A=1000(1+\dfrac{0.06}{4})^{4(4)}=\$1268.99$$

(d) Monthly $n=12$

$$A=1000(1+\dfrac{0.06}{12})^{12(4)}=\$1270.49$$

(e) Daily: $n=365$

$$A=1000(1+\dfrac{0.06}{365})^{365(4)}=\$1271.22$$