Question

In: Finance

You have already saved $6850 to buy a used car. You invest this money in a...

You have already saved $6850 to buy a used car. You invest this money in a certificate of deposit earning 0.30% APR compounded monthly. How many years will it take your account to reach your target of $7275 in order to buy the new car?

Solutions

Expert Solution

First of all we shall learn how to calculate interest on certificate of deposit:

Compute the periodic interest rate by dividing the base annual percentage rate by the number of times each year interest is calculated and added to the CD’s balance (called compounding). For example, if interest on the CD is compounded monthly, divide the base percentage rate by 12 to find the periodic interest rate.

Multiply the previous balance of the CD by the periodic interest rate and add the result to the previous balance to find the new balance of the CD. Suppose you buy a $1,000 CD with an annual base interest rate of 4.8 percent compounded monthly with a periodic rate of 0.4 percent. The interest earned for the first month is $1,000 times 0.4 percent, or $4. The new balance is thus $1,004.

Repeat Step 2 for each succeeding month, but use the balance at the end of the previous month to calculate the current month’s interest.

In this case it is already given that a CD is earning 0.30% APR compounded monthly.

Therefore, to calculate number of years in this case we shall calculate as follows

Formula to calculate interest on CD is

FV = D × (1 + r / n) nt

Where:

FV = Future Value of the CD,

D = Initial deposit amount,

r = Nominal annual interest rate in decimal form,

t = Number of years invested,

n = Number of compounding periods per year.

Initial Amount X (APR/12)

$ 6,850 X 0.025% (0.30 / 12 Months)= $ 1.71 (interest for first month)

$ 6,851.7125 X 0.025% = $ 1.71 (interest for second month)

$ 6,852.42 X 0.025% = $ 1.71 (interest for third month)

and so on.

Therefore as per this calculation it will take 20 Years and 1 month to reach to $ 7,275

I have below attached image for calculation of monthly interest.

FV = Future Value of the CD,

D = Initial deposit amount,

r = Nominal annual interest rate in decimal form,

t = Number of years invested,

n = Number of compounding periods per year.

Initial Amount X (APR/12)

$ 6,850 X 0.025% (0.30 / 12 Months)= $ 1.71 (interest for first month)

$ 6,851.7125 X 0.025% = $ 1.71 (interest for second month)

$ 6,852.42 X 0.025% = $ 1.71 (interest for third month)

and so on.

Therefore as per this calculation


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