Question

You need to have $32750 in 11 years. You can earn an annual interest rate of 6 percent for the first 3 years, 6.6 percent for the next 2 years, and 7.3 percent for the final 6 years. How much do you have to deposit today?

Answer 1

Given,

Future value = $32750

Interest rate for first 3 years (r₁) = 6% or 0.06

Interest rate for next 2 years (r₂) = 6.6% or 0.066

Interest rate for final 6 years (r₃) = 7.3% or 0.073

Solution :-

Deposit today = Future value [(1 + r₁)³ x (1 + r₂)² x (1 + r₃)⁶]

= $32750 [(1 + 0.06)³ x (1 + 0.066)² x (1 + 0.073)⁶]

= $32750 [(1.06)³ x (1.066)² x (1.073)⁶]

= $32750 [1.191016 x 1.136356 x 1.5261539]

= $32750 2.06552443021 = $15855.54

Thus, you have to deposit $15855.54 today.