Question

Calculate the accumulated value of an investment of 4,250 after 7 years assuming the annual effective rate of discount is 6% for the first 2 years, the annual nominal rate of interest compounded monthly 6.6% for the next 3 years and force of interest is 4.5% for the final 2 years. Answer to the nearest cent.

Answer 1

Formula for compound interest is:

A = P x (1+r/n) n x t

A = Accumulated future value of investment

P = Principal amount

n = Annual compounding frequency

t = Time in years

A = $ 4,250 x (1 + 0.06/1) 1 x 2 x (1 + 0.066/12) 3 x 12 x (1 + 0.045/1)1 x 2

   = $ 4,250 x (1 + 0.06) 2 x (1+ 0.0055) 36 x (1 + 0.045)2

   = $ 4,250 x (1.06) 2 x (1.0055) 36 x (1.045)2

= $ 4,250 x 1.1236 x 1.21830127181119 x 1.092025

= $ 6,353.13288095329 or $ 6,353.13

Accumulated value of the investment is $ 6,353.13