Question

(a) How many years will it take for $4000, invested at 4% p.a compounded quarterly to grow to $4880.76? (b) Calculate the nominal annual rate of interest compounded monthly if $4000 accumulates to $5395.4 in five years. (c) Calculate the future value after one year of a debt of $100 accumulated at (i) 12.55% compounded annually; (ii) 12.18% compounded semi-annually.

Answer 1

Explanation:

a.)

`4880.76=4000(1+.04/4)^(4x)\\\\1.22019=1.01^(4x)\\(ln(1.22019))/(ln(1.01))=4x\\x= 4.999999= 5`

b.)

`5395.4=4000(1+x/12)^(12*5)\\1.34885=(1+x/12)^(60)\\\sqrt[60]{1.34885} =1+x/12\\x= 0.0599999772677= .06`

c.)

`\i)\\100*(1+.1255)= 112.55\\\\2)\\100*(1+.1218/2)^2= 112.550881= 112.55`