Question

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On Hubert’s first birthday, his parents deposited $12,000 into a savings account that earns a fixed...

On Hubert’s first birthday, his parents deposited $12,000 into a savings account that earns a fixed rate of 8.50% and compounds interest annually. How much money will Hubert’s account have accumulated by his 21st birthday? (Hint: Round your answer to the nearest dollar.)

$29,438

$61,344

$66,559

$120,000

What-If Scenario 1 What would have been the balance in Hubert’s account if his parents had waited until his 10th birthday to make their initial deposit into the same account?

$66,559

$120,000

$61,344

$29,438

What-If Scenario 2 If Hubert’s parents wanted to accumulate an account balance of $36,000 by his 21st birthday, then how much should they have placed on deposit on his first birthday?

$14,675

$6,490

$7,042

$3,600

Solutions

Expert Solution

Future value = Present value * (1+r)ⁿ

where r is the rate of interest per period, n is the number of periods

Question 1 :

Present value of the deposit = $12,000

Rate of interest = 8.50% per year

period = 20 years (from 1st birthday to 21st)

Future value on 21st birthday = 12,000 * (1+0.085)²⁰

=> 12,000 * 5.112046

=> 61,344.552

=> $61,344 (rounded off)

Question 2 :

Present value of the deposit at 10th birthday = $12,000

Rate of interest = 8.50% per year

period = 11 years (from 10th birthday to 21st)

Future value on 21st birthday = 12,000 * (1+0.085)¹¹

=> 12,000 * 2.453167

=> 29,438.004

=> $29,438 (rounded off)

Question 3 :

Future value of the deposit on 21st birthday= $36,000

Rate of interest = 8.50% per year

period = 20 years (from 1st birthday to 21st)

Future value on 21st birthday = PV * (1+r)ⁿ

36,000 = PV * (1+0.085)²⁰

36,000 = PV * 5.112046

PV = 36,000 / 5.112046

PV = 7,042.190152436031

=> $7,042 (rounded off)

jeff jeffy answered 1 year ago

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