Question

A student deposits $1,642 in the bank that pays 6.2% interest yearly (using yearly compounding). After 5 years he withdraws the money from the account and deposits it in perpetual annuity with interest rate 7.5%, that pays X amount yearly. Find X.

Answer 1

Answer:

the perpetuity will pay the student 166.36 dollar per years

Explanation:

First, we solve for the amount of the original investment after 5 years:

$Principal \: (1+ r)^{time} = Amount$

Principal 1,642.00

time 5.00

rate 0.06200

$1642 \: (1+ 0.062)^{5} = Amount$

Amount 2,218.17

Then, this goes into a perpetual annuity at 7.5%

2,218.17 x 0.075 = 166.3630983 = 166.36

the perpetuity will pay the student 166.36 dollar per years