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Annuities
You'd like to go to Spain in 18 months to visit the places where Game of Thrones was filmed, and you think that you'll need a total of Rp120 million. You have currently Rp20 million in your savings account generating an annual return of 7.5% p.a. compounded quarterly
a) How much extra money you should deposit today so you have enough for the trip?
b) Assume that you actually need the Rp 20 million for something else, so you have to withdraw it from the bank. How much money you should save quarterly instead so you can still afford to travel?
c) After the visit, you love the country so much that you decide to apply for a 1-year scholarship. Fortunately for you, the Spanish government grants it and gives you 2 choices: either receive a lump sum of €30,000 or get 12 monthly payments of €2,550 each. Assuming that you could put the lumpsum in a bank account earning 5% p.a. compounded monthly, which option would you prefer? Why? Quarterly instead so you can still afford to travel?
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