Question

Future value with periodic rates.   Matt Johnson delivers newspapers and is putting away ​$35 at the end of each quarter from his paper route collections. Matt is 8 years old and will use the money when he goes to college in 10 years. What will be the value of​ Matt's account in 10 years with his quarterly payments if he is earning 6.5 ​% ​(APR), 8 % ​(APR), or 13.5 % ​(APR)? What will be the value of​ Matt's account in 10 years with his quarterly payments if he is earning 6.5 ​% ​(APR)? ​$nothing    ​(Round to the nearest​ cent.)

Answer 1

a ) Future value @ 6.5%

Interest rate per annum (r) = 6.5 %

Number of years (n) = 10 years

Number of payment per annum (p) = 4

Interest rate per period = ( Interest rate per annum / Number of payment per annum)

= 6.5% / 4

= 1.625%

Number of period = Number of years * Number of payment per annum

= 10 * 4

= 40

Future value = P * ((1 + r )^{n - 1} ) / r

   = 35 (( 1 + 1.625%)^{40 - 1}) / 1.625%

= $1950.43

b ) Future value @8%

  

Interest rate per annum (r) = 8 %

Number of years (n) = 10 years

Number of payment per annum (p) = 4

Interest rate per period = ( Interest rate per annum / Number of payment per annum)

= 8% / 4

= 2%

Number of period = Number of years * Number of payment per annum

= 10 * 4

= 40

Future value = P * ((1 + r )^{n - 1} ) / r

= 35 ((1 +2%)^{40 - 1} ) / 2%

= $2114.06

  

c ) Future value @ 13.5%

Interest rate per annum (r) = 13.5 %

Number of years (n) = 10 years

Number of payment per annum (p) = 4

Interest rate per period = ( Interest rate per annum / Number of payment per annum)

= 13.5% / 4

= 3.375%

Number of period = Number of years * Number of payment per annum

= 10 * 4

= 40

Future value = P * ((1 + r )^{n - 1} ) / r

= 35 (( 1 +3.375%)^{40 - 1} ) / 3.375%

= $2875.11