Question

What is the present value of an annuity that pays $352 at the beginning of each year for 47 years if the annuity earns 12% annually?

An account pays 2% annual interest compounded monthly. What is the effective interest rate on this account?

If you deposit some money into a bank account today, to the nearest year, how long will it take to triple your deposit if it earns 11% annually?

What is the present value of an annuity that pays $171 at the end of each year for 35 years if the annuity earns 14% annually?

Answer 1

1.Present value of annuity due=(1+interest rate)*Annuity[1-(1+interest rate)^-time period]/rate

=(1.12)*352[1-(1.12)^-47]/0.12

=$352*9.287961147

=$3269.36(Approx).

2.

EAR=(1+APR/m)^m-1
where m=compounding periods

=(1+0.02/12)^12-1

=2.02%(Approx).

3.

We use the formula:
A=P(1+r/100)^n
where
A=future value($3x)
P=present value($x say)
r=rate of interest
n=time period.

3x=x(1.11)^n

3=(1.11)^n

Taking log on both sides;

log 3=n*log 1.11

n=log 3/log 1.11

=11 years(Approx).

4.

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$171[1-(1.14)^-35]/0.14

=$171*7.070045276

=$1208.98(Approx).