Question

How is the answer $115,677.28????

Challenging questions - bonus! 0/5 points Question 10 Note: this is a very challenging question! In 5 years, you will start receiving monthly payments of $600 from a trust fund that one of your great parents set up for you. The first payment will be made at the very end of year 5 and the payments will last for 35 years. You plan to deposit the money you receive every month into a special account right away that pays 6.80% APR with quarterly compounding, Today the account mentioned above has a balance of $10000. Assuming that interest rate will stay constant, what will be the account balance at the end of the 14th year? Answer: * (115677.28) > (8)

Answer 1

Determining the account balance at the end of 14 years;

First, we will calculate the value of current balance of $10000 at the end of 14 years using Compounding formula:-

Future Value = P(1+r)^t

where, P = Principal amount := $10000

r = Periodic Interest rate ;= 0.0680/4 ;= 0.017

t = No of periods ;= 4 quarters * 14 years ;= 56

FV = 10000(1+0.017)⁵⁶

= 10000*2.570238

= $25702.38

Secondly, we will calculate $600 monthly received and invested every month into special account that pays 6.80% with quarterly Compounding. Since, interest will be compounded quarterly, converting monthly deposits into quarterly deposits which is $600*3 = $1800.

As monthly payments is received at the end of 5th year and we have to compute balance at the end of 14th year, the time money deposited will be compounding is 9 years.

Future value of deposits using FV annuity due formula;

$FV= C*[\frac{(1+i)^{n}-1}{i}]*(1+i)$

where, P = Principal amount := $1800

r = Periodic Interest rate ;= 0.0680/4 ;= 0.017

t = No of periods ;= 4 quarters * 9 years ;= 36

FV = 1800 * [ (1 + 0.017)36 - 1 0.017 ]*(1 + 0.017)

2TOO (ΣΤΟΙ) * -2TEST * 0081 = Λ.4

FV = 1800 * 49.9347

FV = $ 89,882.46

So, total amount after 14 years is $ 115,584.84 (89882.46+25702.38)

Note- there is a difference of 92.44 in your answer and mine. Mainly can be because of decimal rounding off. I have taken decimals with 4 digits to compute the answer.

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