Question

1. If the discounted amount is ₱8500 while the discount rate is 22% then what is the future amount of the money?

2. Compute the annuity of the money which has future worth of ₱50 000 in 5 years if it compounded monthly at the rate of 11%?

3. What is the equivalent effective rate of interest compounded quarterly if the nominal rate is 14.5%?

Answer 1

1. discounted amount = 8500

discount rate = 22%

future value = 100%

$100-22=78$

78% = 8500

100% = x

$78$ $*x= 8500*100$

$78x=850000$

$​ \frac{78x}{78} = ​ \frac{850000}{78}$

$x=10897.4359$

The future value is approximately P10897.

2.Future value (FV) = 50000

time n= $5*12=60$

interest rate = 11%

monthly interest rate = $11/100÷12$$=$ 0.009166

present value (PV)

$PV = FV[\frac{1}{(1+r)^n}$ ]

$(1+r)^n= (1+0.009166)$ ⁶⁰ =1.728916

$PV= 50000[\frac{1}{1.728916}]$

= 28919.8595

The present value is approximately 28919.86

3.

Nominal rate (r)= 14.5%

Compounding (m)= 4/yr

effective rate interest (i)

$i= (1+\frac{r}{m}$ ) ^m -1

$i=(1+\frac{0.145}{4}$)⁴ -1

$i=0.15307664$

I= $i*100$

I$= 0.15307664*100$

= 15.307664

The effective interest rate is approximately 15.3077%