Question

At the end of every 3 months, Teresa deposits into an account that pays 5% compounded quarterly. After she puts the accumulated amount into a certificate of deposit paying 8.5% compounded semiannually for When this certificate matures, how much will Teresa have accumulated

Answer 1

Answer:

The amount Teresa will have accumulated when this certificate matures is $2,452.16.

Explanation:

Note: This question is not complete as some important data are omitted. The complete question is therefore provided before answering the question as follows:

At the end of every 3 months, Rita deposits $100 into an account that pays 5% compounded quarterly. After 5 years, she puts the accumulated amount into a certificate of deposit paying 8.5% compounded semiannually for 1 year. When this certificate matures, how much will Teresa have accumulated?

The explanation of the answers is now provided as follows:

Step 1: Calculation of accumulated amount after 5 years.

Since the deposits are paid at the end of every 3 months, the accumulated amount after 5 years can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV5 = P * (((1 + r1)^n1 - 1) / r) ................................. (1)

Where,

FV5 = Future value or accumulated amount after 5 years = ?

P = Quarterly deposit or deposit at the end of every 3 months = $100

r = Quarterly interest rate on the account = Interest rate on the account / Number of quarters in a year = 5% / 4 = 0.05 / 4 = 0.0125

n = number of quarters = 5 years * Number of quarters in a year = 5 * 4 = 20

Substituting the values into equation (1), we have:

FV5 = $100 * (((1 + 0.0125)^20 - 1) / 0.0125) =  $2,256.30

Therefore, the accumulated amount after 5 years is $2,256.30.

Step 2: Calculation of the amount Teresa will have accumulated when this certificate matures.

This can be calculated using the simple future value (FV) as follows:

FVM = FV5 * (1 + R)^N ……………………… (2)

FVM = Accumulated amount at maturity = ?

R = semi-annual interest rate on certificate of deposit = Interest rate on certificate of deposit / Number of semiannuals in a year = 8.5% /2 = 0.085 / 2 = 0.0425

N = number of semiannuals = 1 year * Number of semiannuals in a year = 1* 2 = 2

Substituting the values into equation (2), we have:

FVM = $2,256.30 * (1 + 0.0425)^2 = $2,452.16

Therefore, the amount Teresa will have accumulated when this certificate matures is $2,452.16.