Question

Allison is 26 years old and plans to retire at age 65 with ​$1,90,000 in her retirement account. What amount would she have to set aside now in an investment paying 7​% annual interest if the compounding is done daily ​(assume 365 days in a​ year)?

Answer 1

Answer:

Allison would need to deposit $123,950.50

Step-by-step explanation:

Since we are talking about compounding interest we can use the Exponential Growth formula to calculate this problem. The Formula is the following

$y = a*(1+r)^{t}$

Where:

1. y is the total amount after a given time
2. a is the initial amount
3. r is the interest rate in decimals
4. t is the given time

Assuming the total amount is $1,900,000 (since there is a number missing in the question) then we would first need to calculate the daily interest rate (since we are compounding daily) and the amount of days between her first deposit and her withdraw at age 65.

0.07 / 365 = 0.00019178 daily

(65-26) * 365 = 14,235 days

Now we can plug our values into the formula and solve for the initial amount (a)

$1,900,000= a*(1+0.00019178)^{14235}$

$1,900,000= a*(1.00019178)^{14235}$

$1,900,000= a*15.3287$

$123,950.50 = a$

Allison would need to deposit $123,950.50 into her retirement account today to retire at 65 with $1,900,000.

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