Question

Sophia inherits inherited money from her grandparents. She inherits $100,000 from her grandparents, today. She has exactly 20 years to retire and she decided to put the entire amount into 20 years, 4% annual interest annuity.

A) Assume that she did not deposit any additional amount into this account, compute your account balance by the time she retires. Please compute the problem using a scientific calculator (not a financial one) using the appropriate formulas and show your calculations step by step!

B) Now assume that in addition to this initial $100,000, you also contributed $500 at the end of each month until you retire. Now, using the relevant formulas and a scientific calculator, reproduce Highlight the end balance, total principal, and total interest, step by step please!

Answer 1

A)

Account balance when she retires = $219,112

Future Value of a Single Payment
Formula
FVn	PVo (1+i)^n
FVn		Future Value
Pvo	$100,000.00	Present Value
i	4.00%	Annual Compound interest rate
n	20	number of years
(1+i)	1.0400
(1+i)^n	2.191123
FVn	$219,112.31

B)

Besides the above calculation lets find the FV of $500 deposited each month for 20 years

Future Value of an Annuity
Formula
PMT [ (1+i)^n - 1] / i
Pmt	$500	Payments of a fixed amount
i	0.33%	Interest Rate = 4%/12
n	240	no of payment period = 20*12
1+i	1.0033
(1+i)^n	2.2226
(1+i)^n - 1	1.2226
[ (1+i)^n - 1] / i	366.7746
Future Value	$183,387.31

Hope this helps! In case of any clarifications, kindly use the comment box below