At 21 Julio begins saving 1250 each year until age 35 in an ordinary annuity paying...

At 21 Julio begins saving 1250 each year until age 35 in an ordinary annuity paying 5.7% annual interest compound yearly and then leaves his money in the account until age 65.

Expert Solution


Step 1
Calculation of future value of annuity at the end of 35th year
We can use the future value of annuity formula to calculate this value.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = value of savings at the age of 35 = ?
P = Annual savings = $1250
r = rate of interest per annum = 5.7%
n = no.of years = 15
Future value of annuity = 1250 x {[(1+0.057)^15 -1]/0.057}
Future value of annuity = 1250 x 22.75103
Future value of annuity = $28,438.79
Future value of savings at the age of 35 = $28,438.79

Step 2
Calculation of value of savings at the age of 65
We can use the future value of sum formula to calculate this value.
Future value of sum = P x (1+r)^n
Future value of sum = Future value of value calculated in step 1 at the end of 65th year = ?
P = Value calculated in step 1 = $28438.79
r = rate of interest per annum = 5.7%
n = no.of years = 30
Future value of sum = 28438.79 x (1+0.057)^30
Future value of sum = 150024

The answer is
Value of savings at the age of 65 = $1,50,024

jeff jeffy answered 2 years ago

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