Question

-Jerry calculates that if he makes a deposit of $6 each month at an APR of 4.8%, then at the end of two years he'll have $100. Benny says that the correct amount is $161. The Regular Deposits Rule of Thumb should be helpful here. What was the total amount deposited (ignoring interest earned)?

-Suppose you want to save in order to purchase a new boat. Take the APR to be 8.4%.
If you deposit $100 each month, how much will you have toward the purchase of a boat after three years?

-Suppose you want to save in order to purchase a new boat. Take the APR to be 8.4%.
You want to have $11,000 toward the purchase of a boat in three years. How much do you need to deposit each month?

Answer 1

1) Over the two years, Jerry will have made 24 deposits of $6 for a total of 24*6 = $144

If he had instead deposited the entire $120 at the beginning of the 2 years, he'll earn more interest than if he splits it up monthly.

If the yearly APR is 4.8%, then the monthly interest rate is 4.8%/12 = 0.4% = 0.004. He'll have invested it for 24 months, so

Maximum Balance = $144(1.004)²⁴ = $158.48

This eliminates $161 as a possible amount, since it is more than what he would make with a single lump sum deposit.

Benny is wrong. Jerry would accumulate somewhere between $100 and $158

2) Payment amount , A = $100

r = 8.4/12 = 0.7% = 0.007

number of periods, n = 3 x 12 = 36

FV = $4078.1

3) Payment amount , A = ?

FV = $11,000

r = 8.4/12 = 0.7% = 0.007

number of periods, n = 3 x 12 = 36

A = $269.73