Question

The rickerts decided to set up an account for their daughter to pay for her college education. the day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. beginning with her first birthday, they deposit an additional $750 into the account on each of her birthdays. which expression correctly represents the amount of money in the account n years after their daughter was born?

Answer 1

After n years, the deposit made at birth will have a value equal to;

FV1 = C(1+r)^n = 1000(1+0.018)^n = 1000(1.018)^n

After n years, the  yearly deposits made at every birthday will have a value equal to;

FV2 = P{(1+r)^n-1}/r = 750{(1+0.018)^n-1}/0.018 = 41666.67 {(1.018)^n-1} = 41666.67 (1.018)^n -41666.67

Total FV = FV1+FV2 = 1000(1.018)^n+41666.67(1.018)^n-41666.67 = 42666.67 (1.018)^n - 41666.67