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?

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Business

Gwendolyn Miranda

29 September, 06:54

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?

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Adrianna Nelson · 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