Question

Allen deposits $100 into a fund today and $200 at the end of 30 years. Interest is credited at a quarterly nominal discount rate 6% for the first 10 years, at a semiannually nominal interest rate of 8% for the next 10 years, and at a force of interest of 10% thereafter. Calculate the accumulated value at the end of 40 years.

Answer 1

Value at Year 40 = FV of $ 100deposited today + FV of $ 200 deposited after 30 Years

FV = PV (1+r)^n

FV of $ 100deposited today :

Value after 10 Years = $ 100 ( 1 + 0.015)^40

= $ 100 ( 1.015^40)

= $ 100 * 1.8140

= $ 181.40

Value after 20 Years = $ 181.40 ( 1 + 0.04)^20

= $ 181.40 ( 1.04^20)

=$ 181.40 * 2.1911

= $ 397.47

Value at 40 Years:

Value after 20 Years =$ 397.47 ( 1 + 0.10)^20

= $ 397.47 ( 1.10^20)

=$ 397.47 * 6.7275

= $ 2673.98

FV of $ 200deposited after 30 Years :

Value after 40 Years =$ 200( 1 + 0.10)^10

= $ 200 ( 1.10^10)

=$ 200 * 2.5937

= $ 518.75

Amount after 40 Years:

= FV of $ 100deposited today + FV of $ 200 deposited after 30 Years

= $ 2673.98 + $ 518.75

= $ 3192.73