Question

If $800 is borrowed at 8% interest, find the amounts due at the end of 4 years if the interest is compounded as follows. (Round your answers to the nearest cent.)(i) annually(ii) quarterly(iii) monthly(iv) weekly

Answer 1

Answer:

(i) $133.12

(ii) $297.6

(iii) $300.8

(iv) $301.6

Explanation:

From the compounding formula;

Future value = Present value $(1+\frac{r}{m}) ^{mn}$

where r is the rate, m is the number of payment per year, and n is the number of years.

Interest = future value - present value

Given that present value = $800, r = 8%, n = 4 years.

(i) annually,

m = 1, so that;

Future value = 800$(1.08)^{4}$

                     = $933.12

Interest = $933.12 - $800

             = $133.12

(ii) quarterly,

m = 3, so that;

Future value = 800$(1+\frac{0.08}{3}) ^{(4x3)}$

                      = 800(1.372)

                      = $1097.6

Interest = $1097.6 - $800

             = $297.6

(iii) monthly,

m = 12, so that;

Future value = 800$(1+\frac{0.08}{12}) ^{(4x12)}$

                     = 800(1.376)

                     = $1100.8

Interest = $1100.8 - $800

             = $300.8

(iv) weekly,

m = 54, so that;

Future value = 800$(1+\frac{0.08}{54}) ^{(4x54)}$

                     = 800(1.377)

                     = $1101.6

Interest = $1101.6 - $800

             = $301.6