Question

1. Calculating Interest Rates. Assume the total cost of a college education will be $345,000 when your child enters college in 18 years. You presently have $73,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?
2. Calculating the Number of Periods. At 6.1 percent interest, how long does it take to double your money? To quadruple it?
3. Calculating Interest Rates. According to the Census Bureau, in October 2016, the average house price in the United States was $354,900. In October 2000, the average price was $215,100. What was the annual increase in the price of the average house sold?

Answer 1

Solution :

1) Calculation of Interest rate :

Here,

Annual rate of interest = ( Future value / Present value )^(1/time) - 1

= ( 345,000 / 73,000 )^(1/18) - 1

= 9.01%

2) Calculation of Number of periods :

Here, we use NPER function in Excel to calculate the no. of years as follows :

Number of periods =NPER(rate,pmt,pv,fv)

Where,

rate per period ( rate ) = 6.10%

Payment ( pmt ) = 0

Present value ( pv ) = -$100 ( say )

Future value ( fv ) = $200 ( 2*say )

Now,

Number of periods =NPER(6.10%,0,-100,200) = 11.71 years

Therefore,

It takes 11.71 years to double the money.

Then,

Number of periods =NPER(rate,pmt,pv,fv)

Where,

rate per period ( rate ) = 6.10%

Payment ( pmt ) = 0

Present value ( pv ) = -$100 ( say )

Future value ( fv ) = $400 ( 4*say )

Now,

Number of periods =NPER(6.10%,0,-100,400) = 23.41 years

Therefore,

It takes 23.41 years to quadruple the money.

3) Calculation of Increase in price :

Here,

Annual increase in price = ( Average price in 2016 / Average price in 2000 )^( 1 / Total Years ) - 1

= ( 354900 / 215100 )^( 1 / 16 ) - 1

= 3.179068%

Annual increase in price = 3.18%