How many whole numbers are there with not more than 4 digits?
2 answers:
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Answer:
a) 8.16%
b) $65,762.50
c) $39,701.07
Step-by-step explanation:
Given:
15 years ago, Initial investment = $12500
5 years ago, Investment = $20000
Nominal interest = 8% semi annually for first 10 years
Interest2= 6.5% compunded annually for last five years
a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:
[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1
= 1.0816 - 1
= 0.0816
= 8.16%
The effective annual interesting rate, EAR = 8.16 %
b) To find the amount in my account today.
Let's first find the amount for $12500 for 10 years compounded semi annually
= 12,500 +( 12,500 * 8.160% * 10)
= $ 22,700
Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually
$32,500 + ($32,500 * 6.5% *5)
= $ 43,062.50
Money in account today will be:
$22,700 + $43,062.50
= $65,762.50
c) Let's the amount I should have invested to be X
For first 10 years at 8.160%, we have:
Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X
For next 5 years at 6.5%, we have:
Interest Amount = (X * 6.5% * 5) = 0.325 X
Therefore the total money at the end of 15 Years = 85000
0.8160X + 0.3250X + X = $85,000
= 2.141X = $85,000
X = 85,000/2.141
X = 39,701.074 ≈ $39,700
If I wish to have $85,000 now, I should have invested $39,700 15 years ago
The first figure below shows the graph for problem 5).
The second figure below shows the graph for problem 6).
The second figure below shows the graph for problem 6).