Question

An investment company pays 6% compounded semiannually You want to have $22,000 in the future. (A) How much should you deposit.now to have that amount 5 years from now? (to the nearest cent) (B) How much should you deposit now to have that amount 10 years from now? (Round to the nearest

Answer 1

Explanation:

Firstly, compound interest is defined as:

`a = p {(1 + (r)/(n) )}^(nt)`

Where:

a = final amount

p = principal (original amount)

r = decimal rate of interest

n = repetitions per annum

t = number of years

Knowing this, we replace for the values stipulated and solve.

A. $13,370.07

`22000 = x {(1 + (0.06)/(2) )}^(2 * 5) \\ 22000 = x {(1.03)}^(10) \\ x = \frac{22000}{ {(1.03)}^(10) } \\ x = 16370.07`

B. $12180.87

`22000 = x {(1 + (0.06)/(2) )}^(2 * 10) \\ 22000 = x {(1.03)}^(20) \\ x = \frac{22000}{ {(1.03)}^(20) } \\ x = 12180.87`