Question

You want to buy a new surfboard 12 years from now. You have $600 in the bank today. You can earn 7% on your savings. If the surfboard will cost $5,000, how much will you have to save every year to have enough to buy it? Round your answer to 2 decimals, for example 100.12

Answer 1

Step 1 - First we have to find out the future value of $600 at the end of 12th year at 7% interest rate using future value of sum formula.

Step 2 - Then deduct this future value from $5000 ,the resulting amount will be the future value of yearly savings required.

Step 3 - We can find out this yearly savings using Future value of annuity formula.

Step 1

Future value of sum = P * (1+r)^n

P = amount in bank today = $600

r = interest rate per year = 7%

n = number of years = 12

Future value of sum = 600 * (1+0.07)^12 = $1,351.31

Step 2

Future value of yearly savings required = $5000 - $1351.31 = $3,648.69

Step 3

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

Future value of annuity = value calculated in step 2 = $3648.69

P = Yearly savings required to buy a new surfboard = ?

r = interest rate per year = 7%

n = number of years = 12

$3648.69 = P * {[(1+0.07)^12 -1]/0.07}

$3648.69 = P * 17.88845

P = 203.97

You have to save $203.97 every year to have enough money at the end 12th year to buy a surfboard.