Question

1) Jeff deposits 100 at the end of each year for 13 years into Fund X. Antoinette deposits 100 at the end of each year for 13 years into Fund Y.

Fund X earns an annual effective rate of 15% for the first 5 years and an annual effective rate of 6% thereafter. Fund Y earns an annual effective rate of i.

At the end of 13 years, the accumulated value of Fund X equals the accumulated value of Fund Y. Calculate i.

A. 0.064

B. 0.067

C. 0.070

D. 0.074

E. 0.078

2) Harriet wishes to accumulate $60,000 in a fund at the end of 25 years. She plans to deposit $80 into the fund at the end of each of the first 120 months.

She then plans to deposit $80 + X into the fund at the end of each of the last 180 months. Assume the fund earns interest at an annual effective rate of 3.66%. Determine X.

A. Less than $86

B. At least $86, but less than $88

C. At least $88, but less than $90

D. At least $90, but less than $92

E. At least $92

Answer 1

1]

Accumulated value of Fund X at the end of 5 years is calculated using FV function in Excel :

rate = 15%

nper = 5

pmt = -100 (Yearly deposit. This is entered with a negative sign because it is a deposit into the account)

FV is calculated to be $674.24

Accumulated value of Fund X at the end of 13 years is calculated using FV function in Excel :

rate = 6%

nper = 8 (number of deposits from end of 5th year to end of 13th year = 8)

pmt = -100 (Yearly deposit. This is entered with a negative sign because it is a deposit into the account)

pv = -674.24 (Accumulated value of Fund X at the end of 5 years. This is entered with a negative sign because it is like a deposit into the account)

FV is calculated to be $2,064.38

Now, we calculate the annual effective rate to be earned by Fund Y such that the accumulated value of Fund Y at the end of 13 years is $2,064.38

We calculate the annual effective rate to be earned by Fund Y using RATE function in Excel :

nper = 13

pmt = -100

pv = 0

fv = 2064.38

RATE is calculated to be 0.074

The answer is (D)