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brandon wishes to accumulate 100,000 by making level monthly end of month deposits for 30 years...

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Finance

brandon wishes to accumulate 100,000 by making level monthly end ofmonth deposits for 30 years into an account that earns 5.4%interest convertible monthly. after 10 years the interest rateincreases to 6.6% convertible monthly. what should brandons newdeposit amount be if he wishes to accumulate 100,000 at the end of30 years?

Answer & Explanation Solved by verified expert
4.3 Ratings (917 Votes)

Future value of annuity = P{(1+r)^n-1}/r
here,
Future value = $100,000
rate = 0.054/12=0.0045 per month
time = 30*12=360 months
100,000 = P[{(1+0.0045)^360}-1]/0.0045
100,000 = P*896.6133
100,000/896.6133 = P
$111.53 = P
Monthly installment = $111.53
Future value of this investment after 10 years
Rate = 0.0045 per month
time = 10*12=120 months
Future value after 10 years = 111.53[{(1=0.0045)^120}-1/0.0045
= 111.53*158.6509
= $17,694
Value of $17694 after 20 years (i.e. 30 years from now @ 0.0055(0.066/12) per month)
= 17694*(1+00.55)^240
(this is value of single amount not annuity) = $65,997
After 10 years additional amount (in future value terms)required
= 100,000-65997
= $34,003
Applying the formula of future value again
34003 = P[{(1+0.0055)^240}-1]/0.0055
34003 = P*545.9813
34003/496.34 = P
$68.50 = P
New deposit is $68.5 per month
There may be minor differences due to decimal places.

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Transcribed Image Text

brandon wishes to accumulate 100,000 by making level monthly end ofmonth deposits for 30 years into an account that earns 5.4%interest convertible monthly. after 10 years the interest rateincreases to 6.6% convertible monthly. what should brandons newdeposit amount be if he wishes to accumulate 100,000 at the end of30 years?

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