Question

Starting at age​ 50, a woman puts ​$1400 at the end of each quarter into a retirement account that pays​ 7% interest compounded quarterly. When she reaches age​ 60, she withdraws the entire amount and places it in a mutual fund account that pays​ 9% compounded monthly. From then on she deposits ​$200 in the same mutual fund at the end of each month. How much is in the account when she reaches age​ 65?

Answer 1

(interest compounded quarterly - added at the end of each quarter)

Year	Year Interest	Total Interest	Balance
1	$100.60	$100.60	$1,500.60
2	$107.83	$208.43	$1,608.43
3	$115.58	$324.02	$1,724.02
4	$123.89	$447.90	$1,847.90
5	$132.79	$580.69	$1,980.69
6	$142.33	$723.02	$2,123.02
7	$152.56	$875.58	$2,275.58
8	$163.52	$1,039.10	$2,439.10
9	$175.27	$1,214.37	$2,614.37
10	$187.87	$1,402.24	$2,802.24

Initial investment amount at the age of 50 years : $1,400.00
Interest Rate: 7% (yearly)
Effective Annual Rate: 7.19%
Calculation period: 10 years

At the age of 60 years she can withdraw= $2,802

If she invests same amount in a mutual fund and additional $ 200 at the end of each month from 60 years on wards for a period of another 5 years ( 65 age),

Then her cumulative wealth would be=

(interest compounded monthly - added at the end of each month)

Year	Year Deposits	Year Interest	Total Deposits	Total Interest	Balance
1	$2,400.00	$383.13	$5,202.00	$383.13	$5,585.13
2	$2,400.00	$644.20	$7,602.00	$1,027.33	$8,629.33
3	$2,400.00	$929.77	$10,002.00	$1,957.10	$11,959.10
4	$2,400.00	$1,242.12	$12,402.00	$3,199.22	$15,601.22
5	$2,400.00	$1,583.78	$14,802.00	$4,783.00	$19,585.00

Base amount: $2,802.00
Interest Rate: 9% (yearly)
Effective Annual Rate: 9.38%
Calculation period: 5 years

Her total wealth would be $19,585.