1 IF 100 IS DEPOSITED AT THE END OF EACH MONTH IN A SAVINGS

1- IF $100 IS DEPOSITED AT THE END OF EACH MONTH IN A SAVINGS ACCOUNT THAT PAYS 1% INTEREST PER MONTH STARTING ONE MONTH FROM NOW, HOW MUCH MONEY WILL BE IN THE ACCOUNT AT THE END OF SEVEN YEARS?

2- TO RAISE MONEY FOR A NEW HOME, YOUR DAUGHTER ASKS YOU TO LEND HER “SOME” MONEY. SHE OFFERS TO PAY YOU $50,000 AT THE END OF FOUR YEARS. HOW MUCH SHOULD YOU LOAN HER NOW IF YOU WANT TO RECEIVE 5% INTEREST PER YEAR? NOTE: THE ANSWER IS NOT $ 0.

3- A FUND ESTABLISHED TO PRODUCE A DESIRED AMOUNT OF MONEY AT THE END OF A GIVEN TIME PERIOD, BY MEANS OF SERIES OF PAYMENTS THROUGHOUT THE PERIOD IS CALLED A SINKING FUND.   A SINKING FUND IS TO BE ESTABLISHED TO ACCUMULATE MONEY TO REPLACE A $12,000 MACHINE. IF THE MACHINE IS TO BE REPLACED AT THE END OF 10 YEARS, HOW MUCH MONEY SHOULD BE DEPOSITED IN THE SINKING FUND EACH YEAR,STARTING IN YEAR 1? USE AN INTEREST RATE OF 8%.

4- AN INDIVIDUAL IS CONSIDERING THE PURCHASE OF AN USED AUTO-MOBILE. THE TOTAL PURCHASE PRICE IS $6200. WITH A $1240 DOWN PAYMENT AND THE BALANCE PAID IN 48 EQUAL MONTHLY PAYMENTS AT AN INTEREST RATE OF 1% PER MONTH, COMPUTE THE MONTHLY PAYMENT. THE PAYMENTS START IN THE FIRST MONTH AND ARE DUE AT THE END OF EACH SUCCESSIVE MONTH.

5- A RETIREMENT FUND EARNS 1.5% INTEREST COMPOUNDED QUARTERLY. IF $ 400 IS DEPOSITED EVERY 3 MONTHS FOR 25 YEARS, THE AMOUNT IN THE FUND AT THE END OF 25 YEARS IS NEAREST TO:

$ 50,000                            c. $ 100,000

$ 75,000                           d.   $ 125,000

Solution

4)

The correct answer is option A: $130.45

Calculation:

The amount to be repaid in 48 monthly payments = Cost of the automobile - Down Payment ($1240)

A = P(A/P,i,n)

P = 6200-1240 = $4960

n = 48

i = 1% per month

Hence A= 4960( A/P, 1%, 48)

5)

Answer:

Interest Rate (r) = 8% compounded quarterly or 8%/4 = 2% perquarter or per 3 months

Payment (C) = $400 per quarter or per 3 months

Time (t) = 25 years or 25*4 = 100 quarters

Future Value (FV) =?

It is the case of future value ordinary annuity, we knowthat;

FV = C * [(1+r) ^t – 1)] / r

FV = 400 * [(1+0.02) ¹⁰⁰ – 1)] / 0.02

FV = 400 * [(1.02) ¹⁰⁰ – 1)] / 0.02

FV = 400 * [7.244646 – 1] / 0.02

FV = 400 * [6.244646] / 0.02

FV = 400 * 312.2323

FV = $124,892.92 will be collected at the end of 25years.

A = 4960 (0.0263)

A = $130.45