Question

MATHEMATICS OF BUSINESS AND FINANCE

(A) How much should Taylor's dad invest into a savings account today, to be able to pay for Taylor's rent for the next six years if rent is $900 payable at the beginning of each month? The savings account earns 3.75% compounded monthly.

(B) Since the birth of her daughter, 20 years ago, Alexis has deposited $190.00 at the beginning of every month into an RESP. The interest rate on the plan was 3.20% compounded monthly for the first 9 years and 4.40% compounded monthly for the next 11 years.

1. Calculate the value of the fund today (the end of a 20-year term)

2. How much of this is interest?.

Answer 1

A). Annuity due: PMT = 900; N = 6*12 = 72; rate = 3.75%/12 = 0.313%, Type = 1, (or Begin mode for annuity due), CPT PV.

PV = 58,127.72

B). FV of monthly savings at the end of 9 years:

PMT = 190; N = 9*12 = 108; rate = 3.20%/12 = 0.267%, Type = 1 (or Begin mode for annuity due), CPT FV.

FV = 23,807.10

PV = 23,807.10; PMT = 190; N = 11*12 = 132; rate = 4.4%/12 = 0.367%, Type = 1 (or Begin mode for annuity due), CPT FV.

FV = 70,897.20

i). Value of the fund today = 70,897.20

ii). Total amount deposited in 20 years = 20*12*190 = 45,600

Interest earned over 20 years = Future value - total amount deposited

= 70,897.20 - 45,600 = 25,297.20