Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an
additional $20,000 to that account. You earned 8%, compounded semi-annually, for the first ten years,
and 6.5%, compounded annually, for the last five years.
Required:
a) What is the effective annual interest rate (EAR) you would get for your investment in the first 10
years?
b) How much money do you have in your account today?
c) If you wish to have $85,000 now, how much should you have invested 15 years ago?
Answers
Given : Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, added an additional $20,000 to that account. Earned 8%, compounded semi-annually, for the first ten years, and 6.5%, compounded annually, for the last five years.
To find : What is the effective annual interest rate (EAR)
Explanation:
P = 12500
Rate of interest for 1st 10 years = 8 %
compounded semi-annually
time = 10 years
Amount after 10 Years = 12500 ( 1 + 8/200)²ˣ¹⁰
= 27389
interest earned = 27389 - 12500 = 14889
(14889/12500) * 10 = 11.9 %
effective annual interest rate (EAR) = 11.9 %
6.5%, compounded annually, for the last five years.
P = 20000 + 27389 = 47389
47389 ( 1 + 6.5/100)⁵ = 64927
64927 is have in your account today
to have 85000 , 62040 required 5 years ago
62040 - 20000 = 42040 required 5 years ago
27389 was amount 5 years ago
Extra amount required 5 years ago = 14651
Amount added = (12500/27389) * 14651 = 6686
6686 more amount required to be Deposited
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