Question

Calculate the following:a )Suppose you wish to raise some money for your favorite local charity. This charity needs $50,000 a year to run their operation and you want to make sure that they are ensured an annual payment of this amount from now on for every in the foreseeable future. Given an interest rate of 5%, how much would you have to fund this perpetuity to guarantee this charity a payment of $50,000 per year?b)You decide to put $1,000 in a new bank account and don’t plan to withdraw the money for 10 years. If your bank does continuous compounding and the interest rate is 1%, what will be the future value of this bank account in 10 years?

Answer 1

Answer:

A.- we need to fund 1,000,000 to achieve a 50,000 dollar perpetuity.

B.- There will be 1,105 dolalrs after 10 years.

Explanation:

Formula for perpetuity:

annuity/rate = principal

50,000/0.05 = 1,000,000

we need to fund 1,000,000 to achieve a 50,000 dollar perpetuity.

B.- continuous interest formula:

$Principal \times e^{rate\times time}  = Amount$

we plug our values:

we deposit 1,000 dollar for 10 years at 1% rate

$1,000 \times e^{0.01 \times 10}  = Amount$

And now we solve:

$1,000 \times e^{0.1}  = Amount$

Amount = 1,105.170918 = 1,105