Clarissa want to fund a growing perpetuity that will pay $5000 per year to a local museum starting next year. she wants the annual amount paid to the museum to grow by 5% per year. given that the interest rate is 8% how much does she need to fund this perpetuity?

Clarissa needs to fund the growing perpetuity by $166666.67

Explanation:

A perpetuity is an investment that will give a future series of infinite payments so if the perpetuity gives you a periodic growth rate then you find the difference between the interest rate and the growth rate then use the perpetuity formula which is:

Pv = C/(i-g)

where Pv is the present value of the perpetuity which will be the initial investment.

C is the periodic payments that will be received in future in this case $5000

i is the interest rate given for the perpetuity which is 8%

g is the growth rate per fixed period which is 5%

thereafter we substitute on the above mentioned formula:

Pv= $5000/(8%-5%) then compute

Pv = $166666.67 which will be the initial investment for Clarissa to be paid $5000 per year until she dies.

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