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1)A couple decides to save money for their child's first-year college tuition
1)A couple decides to save money for their child's first-year college tuition. The parents will deposit 30,000 after n months from today and another 50,000 after 2n months from today.
All deposits earn interest at a nominal annual rate of 3.9%, compounded monthly.
Calculate the maximum integral value of n such that the parents will have accumulated at least 90,000 after 3n months from today.
a) 26
b) 29
c) 32
d) 35
e) 40
2) An annuity pays $1800 per quarter for 55 years with the first payment on April 1, 2017. Given an annual nominal rate of interest of 3.6% compounded quarterly, find the PV of this annuity on 1/1/2017
Expert Solution
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2)
The present value is computed as follows:
Present value = Quarterly payment x [ (1 – 1 / (1 + r)n) / r ]
r will be as follows:
= 3.6% / 4 (Because the interest is compounded quarterly, hence r is divided by 4)
= 0.9% or 0.009
n will be as follows:
= 55 x 4 (Because the interest is compounded quarterly, hence n is multiplied by 4)
= 220
So, the present value will be as follows:
= $ 1800 x [ (1 - 1 / (1 + 0.009)220 ) / 0.009 ]
= $ 1,800 x 95.63360734
= $ 172,140.49 Approximately
Do ask in case of any query
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