Question

1. The number of years it will take for $490 to grow to $1,090.76 at 7 percent compounded annually is how many years

2. The annual interest rate compounded annually at which 510 must be invested for it to grow to $1.993.67 in 15 years is what?

3. The present value of $900 to be received 14 years from now discounted back to the present at 9 percent is ?

4. Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $320000 Rolls-Royce Phantom. Jack currently has $39840 that he may invest. He has found a mutual fund that pays 5 percent annual interest in which he will place the money. How long will it take Jack to win Jill's hand in marriage? ignore taxes and inflation

5. If you were offered $251.80 12 years from now in return for an investment of $100 currently, what annual rate of interest would you earn if you took the offer?

Answer 1

1)

Future value = Present value * (1 + interest rate)^{no of periods}

$1090.76 = $490 * (1 + 7%)^{no of periods}

$1090.76 / $490 = (1 + 7%)^{no of periods}

Applying log on both sides

log($1090.76 / $490) = log(1 + 7%)^{no of periods}

log($1090.76 / $490) = no of periods * log(1 + 7%)

No of periods = 11.83 periods or 11 years 10 months

2)

Future value = Present value * (1 + interest rate)^{no of periods}

Let interest rate = X

$1993.67 = $510 * (1 + X%)¹⁵

$1993.67 / $510 = (1 + X%)¹⁵

Applying log on both sides

log ($1993.67 / $510) = log(1 + X%)¹⁵

log ($1993.67 / $510) = 15 * log(1 + X%)

log ($1993.67 / $510) / 15 = log(1 + X%)

0.03947 = log(1 + X%)

(1 + X%) = 10^0.03947

(1 + X%) = 1.0951

Interest rate(X) = 0.0951 or 9.51%

3)

Present value = Future value /  (1 + interest rate)^{no of periods}

Present value = $900 / (1 + 9%)¹⁴

Present value = $269.32

4)

Future value = Present value * (1 + interest rate)^{no of periods}

$320,000 = $39,840 * (1 + 5%)^{no of periods}

$320,000 / $39,840 = (1 + 5%)^{no of periods}

Applying log on both sides

log($320,000 / $39,840) = log(1 + 5%)^{no of periods}

log($320,000 / $39,840) = no of periods * log(1 + 5%)

No of periods = 42.70 periods or 42 years 8 & half months

It will take Jack 42.70 periods or 42 years 8 & half months to win Jill's hand in marriage

5)

Future value = Present value * (1 + interest rate)^{no of periods}

Let interest rate = X

$251.80 = $100 * (1 + X%)¹²

$251.80 / $100 = (1 + X%)¹²

Applying log on both sides

log ($251.80 / $100) = log(1 + X%)¹²

log ($251.80 / $100) = 12 * log(1 + X%)

log ($251.80 / $100) / 12 = log(1 + X%)

0.03342 = log(1 + X%)

(1 + X%) = 10^0.03342

(1 + X%) = 1.07999

Interest rate(X) = 0.07999 or 7.999% 8%