Question

On January 1, 1518, Dracky Lou deposited £17 into an account earning an annual interest rate of 3%. Dracky Lou then took a long nap in his coffin, and woke up on January 1, 2018. Dracky Lou now plans to make the following expenditures using money from this account: On January 1, 2018, Dracky wishes to purchase a Blood Bank for £12.5 million. On January 1, 2118, Dracky wishes to purchase and modernize a crypt in Bucharest Romania. He estimates that the cost will be £225 million. Every year for the each of the next 30 years, Dracky Lou wishes to donate £1 million to his favorite author, Stephanie Niyer. The first donation will be on January 1, 2019. On January 16, 2118 Dracky Lou plans to take another snooze. If he next wakes on January 1, 2218, how much money will he have left in his account? Assume a 3% annual interest rate throughout.

Please show work including equations used!

Answer 1

The formula for compound interest amount is:
A= P * (1+r)^n
Where
A is the total value of the investment
P is the principal invested
r is the rate of interest
n is the number of years

The number of years Dracky Lou sleeps for is 2018-1518 = 500
Hence the value of investment in when he wakes up is:
A=17*(1+0.03)^500
A=44571913 or 44.57 Million Euro
He spends 12.5 Million on 1st Jan, 2018 hence the amount left is 32071913 or 32.07 Million Euro
We can assume this as the new principal on which the interest will be compounded hence on 1st Jan 2019 the amount will be:
A=32071913 * 1.03
A=33034070 or 33.03 Million Euro, He then donates 1 Million Euro hence has left 32.03 Million Euro which will again act as Principal for 1st Jan 2020
Same way
on 1st Jan 2020
A=32034070 * 1.03
A=32995092 or 32.99 Million Euro out of which again 1 Million Euro is donated and he has 31.99 Million Euro to generate interest for the next year
This will continue till 2048 when the 30th Donation is made after which he will have 30.27 Million Euro left, this can be calculated by iterating the same calculation method as above
This amount is reinvested and again used on 2118. Lets calculate the value of investment on 1st Jan 2118 below:
n= 2118-2048 = 70 years
A= 30.27 * (1+0.03) ^ 70
A= 239.6846 Million Euro
So he has 239.6725 Million Euro on 1st Jan 2118 and spends 225 Million Euro on the same day. Hence he now has 14.6846 Million Euro left to be invested back and goes off to sleep for the next 100 years
When he wakes up on 1st Jan 2218 he will have the following value of investment:
A= 14.6846 * (1+0.03)^100
A= 282.218 Million Euro which is the answer to this question