Question

please write in text not in handwriting since its hard to read from a paper pic and i need an explanation for each problem thank you

1. You are planning to accumulate ¥14,000,000 to purchase a home in Tokyo in 8 years with Dia-Ichi Kangyo Bank. For the next 8 years, you earn an annual return of 12% compounded semiannually. How much should you deposit with Dia-Ichi Kangyo Bank every six months?

2 Chicago Equity Partners plans to accumulate $46,275,255 towards structuring a real estate investment trust by depositing $1,500,000 at the end of each year with JPMorganChase. If Chicago Equity Partners earns 16% compounded annually on the deposited funds, how many deposits must it make?

Answer 1

1]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. We need to calculate this.

r = periodic rate of interest. This is (12%/2) = 6%. We divide by 2 since we need to convert the annual rate into semiannual rate)

n = number of periods. This is 8 * 2 = 16 (there are 8 years, or 16 semiannual periods in the investment period)

¥14,000,000 = P * [(1 + 6%)¹⁶ - 1] / 6%

P = ¥14,000,000 * 6% /  [(1 + 6%)¹⁶ - 1]

P = ¥545,330.01

Amount to deposit every six months =  ¥545,330.01

2]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $1,500,000.

r = periodic rate of interest. This is 16%

n = number of periods.  We need to calculate this.

$46,275,255 = $1,500,000 * [(1 + 16%)ⁿ - 1] / 16%

[(1 + 16%)ⁿ - 1] = ($46,275,255 * 16% / $1,500,000)

1.16ⁿ = (1 + ($46,275,255 * 16% / $1,500,000))

n = log_1.16(1 + ($46,275,255 * 16% / $1,500,000))

n = 12

It must make 12 deposits