Question

a) A loan has a stated annual rate of 15.07%. If the loan payments are made monthly and interest is compounded monthly, what is the effective annual rate of interest?
b) You invest $460.00 at the beginning of every year and your friend invests $460.00 at the end of every year. If you both earn an anual rate of return of 11.07%, how much more money will you have after 15.0 years?
c) You currently have $3,531.00 in a retirement Savings account that earns an annual return of 10.16%. You want to retire in 49 years with $1,000,000. How much more do you need to Save at the end of every year to reach your retirement goal?
d) You currently owe $2,085.00 of your credit card that charges an annual interest rate of 19.42%. You make $152.00 of new charges every month and make a paayment of $269.00 every month. What will your credit card balance be in three months?
e)You would like to retire in 27 years. The expected rate of inflation is 1.44% per year. You currently have a standard of living that requires $9.690.00 of monthly expenses. Assuming you want to maintain the same standard of living in retirement, what are your monthly expenses expected to be the first year of retirement?

Answer 1

a) Effective annual rate of interest= (1+r/n)^n-1

=(1+15.07/12)^12-1

=(1+1.2558%)^12-1

=1.012558^12-1

1.161553-1

=0.161553

ie 16.1553%

b) let us first calculate our investment value using formula of annuity due

FV(annuity) = A[(1+r)^n - 1 /r] (1+r)

=460[(1+11.07%)^15 -1/11.07%] (1+11.07%)

=460[(1.1107)^15 - 1 /0.1107] (1.1107)

=460[4.83-1 / 0.1107](1.1107)

=460(34.59846)(1.1107)

=17677.11$

our friend's futue value

FV(annuity) = A[(1+r)^n - 1 /r]

=460[(1+11.07%)^15 -1/11.07%]

=460(34.59846)

=15915.29$

c) 1000000 = 3531(1+10.16%)^49 + A[(1+10.16%)^49 - 1/ 10.16%)

=1000000 = 3531(1.1016)^49 + A[(1.1016)^49-1/0.1016]

=1000000 = 3531(114.5968) + A[(114.5968-1/0.1016]

=1000000 = 404641.2 + A(1118.079)

A = 532.4838$

d) repayment schedule

Year	opening balance	Instalment	Interest@ 1.6183%	Towards principal	New charge	Closing balance
1	2085	269	34	235	152	2002
1	2002	269	32	237	152	1917
3	1917	269	31	238	152	1831