As a part of your savings plan at work, you have been depositing $250 per quarter in a savings account earning 8% interest compounded quarterly for the last 10 years. You will retire in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by increasing your contribution every four months from $250 to $500. Additionally, you have just inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually for the next 15 years. How much money will you have in savings when you retire 15 years from now?
A) $126,862
B) $73,012
C) $161,307
D) $194,415

Question

Quizplus · Accepted Answer

First, let's calculate the amount of savings from the quarterly deposits over the last 10 years. We can use the formula for compound interest, where A is the final amount, P is the principal (initial deposit), r is the interest rate, and n is the number of times compounded per year:

A = P(1 + r/n)^(nt)

Quarterly deposits of $250 per quarter for 10 years is a total of 40 deposits. Plugging in the values, we get:

A = 250(1 + 0.08/4)^(4*10) 
A = 250(1.02)^40 
A = 250(2.20804) 
A = $552,011.18

Next, we need to calculate the savings with the increased contributions of $1,000 to $2,000 per year, where the contribution increases every four months from $250 to $500. This will result in a total of 60 deposits (15 years x 4 deposits per year). To simplify the calculation, we can find the average contribution per deposit:

($250 + $500)/2 = $375

Using the same compound interest formula, we can calculate the total savings from these deposits:

A = 375(1 + 0.08/4)^(4*15) 
A = 375(2.70381) 
A = $1,014,056.28

Finally, we need to add the $10,000 inheritance, which will earn interest at 12% compounded annually over the next 15 years. Using the compound interest formula again:

A = 10,000(1 + 0.12)^15 
A = 10,000(4.53161) 
A = $45,316.12

Adding up all three amounts:

$552,011.18 + $1,014,056.28 + $45,316.12 = $1,611,383.58

Therefore, the answer is choice C: $161,307.

As a Part of Your Savings Plan at Work, You