Answer:
- Christina: $50,859.82 on deposits totaling $5400.
- Adam: $29,503.37 on deposits totaling $10800.
Explanation:
You want to compare the final values and amounts contributed to two accounts. Each involves an ordinary annuity with $150 payments made quarterly, earning 10% interest compounded quarterly. Christina's account has payments made for 9 years, then earns interest at the same rate for 18 more years with no additional payments. Adam's account has payments made for 18 years.
Formulas
The value of an ordinary annuity with payments P made n times per year earning interest at rate r compounded n times per year for t years is ...
A = P((1 +r/n)^(nt) -1)/(r/n)
The value of an account with principal P earning interest at rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
You may notice some similarities in the formulas.
Christina's account
The balance in Christina's account after 9 years of making payments will be ...
A = 150((1 +0.10/4)^(4·9) -1)/(0.10/4) = 150(1.025^36 -1)/0.025)
A = 8595.21
When that is left for 18 more years earning interest at the same rate, the final balance is ...
A = 8595.21(1.025^72) = 50859.82
The payments she made total 36×150 = 5400.
Christina will have $50,859.82 in her account after 27 years. She deposited $5,400 in total.
Adam's account
Adam makes the same deposits for twice as long. His ending balance will be the balance after 18 years.
A = 150((1 +0.10/4)^(4·18) -1)/(0.10/4) = 150(1.025^72 -1)/0.025)
A = 29503.37
He made payments totaling twice what Christina's were.
Adam will have $29,503.37 in his account at the end of 27 years. He deposited $10,800 in total.
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Additional comment
Using the exact amount computed for Christina's annuity, without rounding to the penny, her final balance comes to 1 cent more. In practice, the balance would probably be rounded to the penny each quarter, so the result may be several cents different than these calculations.